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1.
Bruno Kramm 《manuscripta mathematica》1973,10(2):163-189
The notion of deformations of germs of k-analytic mappings generalizes the one of deformations of germs of k-analytic spaces. Using algebraic terms, we prove:
- The morphism f: A→B of analytic algebras is rigid, iff it is infinitesimally rigid. Moreover, this is equivalent to ExA (B,B)=0. This theorem generalizes a result of SCHUSTER [11].
- Let A be a regular analytic algebra. Then f is rigid iff there exists a rigid analytic algebra Bo such that f is equivalent to the canonic injection A→A?Bo.
- If f is “almost everywhere” rigid or smooth, then the injection Ext B l (ΩB|A, Bn)→ExA(B, Bn) is an isomorphism.
2.
Let ? be a ring containing a nontrivial idempotent. In this article, under a mild condition on ?, we prove that if δ is a Lie triple derivable mapping from ? into ?, then there exists a Z A, B (depending on A and B) in its centre 𝒵(?) such that δ(A + B) = δ(A) + δ(B) + Z A, B . In particular, let ? be a prime ring of characteristic not 2 containing a nontrivial idempotent. It is shown that, under some mild conditions on ?, if δ is a Lie triple derivable mapping from ? into ?, then δ = D + τ, where D is an additive derivation from ? into its central closure T and τ is a mapping from ? into its extended centroid 𝒞 such that τ(A + B) = τ(A) + τ(B) + Z A, B and τ([[A, B], C]) = 0 for all A, B, C ∈ ?. 相似文献
3.
Let ℒ and ? be propositional languages over Basic Propositional Calculus, and ℳ = ℒ∩?. Weprove two different but interrelated
interpolation theorems. First, suppose that Π is a sequent theory over ℒ, and Σ∪ {C⇒C′} is a set of sequents over ?, such that Π,Σ⊢C⇒C′. Then there is a sequent theory Φ over ℳ such that Π⊢Φ and Φ, Σ⊢C⇒C′. Second, let A be a formula over ℒ, and C
1, C
2 be formulas over ?, such that A∧C
1⊢C
2. Then there exists a formula B over ℳ such that A⊢B and B∧C
1⊢C
2.
Received: 7 January 1998 / Published online: 18 May 2001 相似文献
4.
Let E,F be two Banach spaces,B(E,F),B+(E,F),Φ(E,F),SΦ(E,F) and R(E,F) be bounded linear,double splitting,Fredholm,semi-Frdholm and finite rank operators from E into F,respectively. Let Σ be any one of the following sets:{T ∈Φ(E,F):Index T=constant and dim N(T)=constant},{T ∈ SΦ(E,F):either dim N(T)=constant< ∞ or codim R(T)=constant< ∞} and {T ∈ R(E,F):Rank T=constant< ∞}. Then it is known that Σ is a smooth submanifold of B(E,F) with the tangent space TAΣ={B ∈ B(E,F):BN(A)-R(A) } for any A ∈Σ. However,for ... 相似文献
5.
《Quaestiones Mathematicae》2013,36(4):573-586
AbstractA Banach algebra element a ∈ A is said to be “polynomially Riesz”, relative to the homomorphism T : A → B, if there exists a nonzero complex polynomial p(z) such that the image T p(a) ∈ B is quasinilpotent. 相似文献
6.
Denny H. Leung 《Mathematische Nachrichten》1990,149(1):177-181
We consider a Gelfand-Phillips type property for the weak topology. The main results that we obtain are (1) for certain Banach spaces, E?? F inherits this property from E and F, and (2) the spaces Lp(μ, E) have this property when E does. A subset A of a Banach space E is a limited set if every (bounded linear) operator T:E → c0 maps A onto a relatively compact subset of c0. The Banach space E has the Gelfand-Phillips property if every limited set is relatively compact. In this note, we study the analogous notions set in the weak topology. Thus we say that A ? E is a Grothendieck set if every T: E → c0 maps A onto a relatively weakly compact set; and E is said to have the weak type GP property if every Grothendieck set in E is relatively weakly compact. In the papers [3, 4 and 6], it is shown among other results that the ?-tensor product E and the spaces Lp(μ, E) inherit the Gelfand-Phillips property from E and F. In this paper, we study the same questions for the weak type GP property. It is easily verified that continuous linear images of Grothendieck sets are Grothendieck and that the weak type GP property is inherited by subspaces. Among the spaces with the weak type GP property one easily finds the separable spaces, and more generally, spaces with a weak* sequentially compact dual ball. Also, C(K) spaces where K is (DCSC) are weak type GP (see [3] and the discussion before Corollary 4 below). A Grothendieck space (a Banach space whose unit ball is a Grothendieck set) has the weak type GP if and only if it is reflexive. 相似文献
7.
Let R be an associative ring with 1; A, B ⊴ R be its ideals; C(n, R, A) be the full congruence subgroup of level A in GL(n, R); and E(n, R, A) be the relative elementary subgroup of level A. We present a very easy proof of the following commutator formula: [E(n, R, A),C(n, R, B)] = [E(n, R, A), E(n, R, B)] for all commutative rings based exclusively on the absolute standard commutator formula and its non-commutative counterparts.
This generalizes and strengethens Mason and Stothers’ results, our results, and those of Hazrat and Zhang. For comaximal ideals
A + B = R, we show that this commutator is E(n, R, AB + BA). 相似文献
8.
Let Aj, Bj be complex B-spaces, j = 0, 1, Aθ and Bθ–the complex-interpolation spaces generated by the couples (A0, A1) and (B0, B1), resp., by CALDERON'S/LIONS'S method. Let T: A0 ∧ A1 → B0 → B1 be an operator satisfying some conditions such as continuity, estimates etc. in terms of the norms of Aj, Bj (j = 0, 1). We consider the question which one of these properties is inherited to T when A0 → A1 and B0 → B1 are equipped with the norm of Aθ and Bθ. 相似文献
9.
Characterizations for Besov spaces and applications. Part I 总被引:1,自引:0,他引:1
The main theorem of this paper gives a characterization for holomorphic Besov space Bp(D) over a large class of bounded domains D in , which states that there is a bounded linear operator so that PVD=I on Bp(D), where P is the Bergman projection, and is the biholomorphic invariant measure with K(z,z) being Bergman kernel function for D. Moreover, some application for characterizing Schatter von Neumann p-class small Hankel operation is given as a direct consequence of this theorem. 相似文献
10.
Let Alg? be a reflexive algebra on a Hilbert space H. We say that a linear map δ: Alg??→?Alg? is derivable at Ω?∈?Alg? if δ(A)B?+?Aδ(B)?=?δ(Ω) for every A, B?∈?Alg? with AB?=?Ω. In this article, we give a necessary and sufficient condition for a map δ on Alg? to be derivable at Ω. In particular, we show that every linear map δ derivable at Ω?≠?0 from an irreducible CDC algebra (in particular, a nest algebra) into itself is a derivation. Moreover, if Alg? is a CSL algebra, and if for some nontrivial projection P?∈??, PΩP and (I???P)Ω(I???P) are left or right separating points in PAlg?P and (I???P)Alg?(I???P) respectively, then a linear map δ on Alg? is derivable at Ω if and only if δ is a derivation. 相似文献
11.
Let A and B be C*-algebras. A linear map T : A → B is said to be a *-homomorphism at an element z ∈ A if ab* = z in A implies T (ab*) = T (a)T (b)* = T (z), and c*d = z in A gives T (c*d) = T (c)*T (d) = T (z). Assuming that A is unital, we prove that every linear map T : A → B which is a *-homomorphism at the unit of A is a Jordan *-homomorphism. If A is simple and infinite, then we establish that a linear map T : A → B is a *-homomorphism if and only if T is a *-homomorphism at the unit of A. For a general unital C*-algebra A and a linear map T : A → B, we prove that T is a *-homomorphism if, and only if, T is a *-homomorphism at 0 and at 1. Actually if p is a non-zero projection in A, and T is a ?-homomorphism at p and at 1 ? p, then we prove that T is a Jordan *-homomorphism. We also study bounded linear maps that are *-homomorphisms at a unitary element in A. 相似文献
12.
It is shown that a Banach space E has type p if and only for some (all) d ≥ 1 the Besov space B(1/p – 1/2)d p,p (?d ; E) embeds into the space γ (L2(?d ), E) of γ ‐radonifying operators L2(?d ) → E. A similar result characterizing cotype q is obtained. These results may be viewed as E ‐valued extensions of the classical Sobolev embedding theorems. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
14.
Let A be a normal operator in ??(H), H a complex Hilbert space, and let ? A = ? {AX - XA:X ∈ ??(H)} be the commutator subspace of ??(H) associated with A. If B in ??(H) commutes with A, then B is orthogonal to ?A with respect to the spectral norm; i.e., the null operator is an element of best approximation of B in ? A. This was proved by J. Anderson in 1973 and extended by P. J. Maher with respect to the Schatten p-norm recently. We take a look at their result from a more approximation theoretical point of view in the finite dimensional setting; in particular, we characterize all elements of best approximation of B in RA and prove that the metric projection of H onto ?A is continuous. 相似文献
15.
J. K. Brooks Kazuyuki Saitô JD Maitland Wright 《Rendiconti del Circolo Matematico di Palermo》2003,52(1):5-14
LetA be aC*-algebra with second dualA″. Let (φ
n)(n=1,...) be a sequence in the dual ofA such that limφ
n(a) exists for eacha εA. In general, this does not imply that limφ
n(x) exists for eachx εA″. But if limφ
n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ
n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for
positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem. 相似文献
16.
Leonid A. Kurdachenko Alexey V. Sadovnichenko Igor Ya. Subbotin 《Central European Journal of Mathematics》2009,7(2):176-185
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dim
F
(BFG/B) is finite. A subspace B is called almost G-invariant, if dim
F
(B/Core
G
(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
相似文献
17.
TieXin Guo 《中国科学A辑(英文版)》2008,51(9):1651-1663
Let (Ω,A,μ) be a probability space, K the scalar field R of real numbers or C of complex numbers,and (S,X) a random normed space over K with base (ω,A,μ). Denote the support of (S,X) by E, namely E is the essential supremum of the set {A ∈ A: there exists an element p in S such that X
p
(ω) > 0 for almost all ω in A}. In this paper, Banach-Alaoglu theorem in a random normed space is first established as follows: The random closed unit
ball S
*(1) = {f ∈ S
*: X
*
f
⩽ 1} of the random conjugate space (S
*,X
*) of (S,X) is compact under the random weak star topology on (S
*,X
*) iff E∩A=: {E∩A | A ∈ A} is essentially purely μ-atomic (namely, there exists a disjoint family {A
n
: n ∈ N} of at most countably many μ-atoms from E ∩ A such that E = ∪
n=1∞
A
n
and for each element F in E ∩ A, there is an H in the σ-algebra generated by {A
n
: n ∈ N} satisfying μ(FΔH) = 0), whose proof forces us to provide a key topological skill, and thus is much more involved than the corresponding
classical case. Further, Banach-Bourbaki-Kakutani-Šmulian (briefly, BBKS) theorem in a complete random normed module is established
as follows: If (S,X) is a complete random normed module, then the random closed unit ball S(1) = {p ∈ S: X
p
⩽ 1} of (S,X) is compact under the random weak topology on (S,X) iff both (S,X) is random reflexive and E ∩ A is essentially purely μ-atomic. Our recent work shows that the famous classical James theorem still holds for an arbitrary
complete random normed module, namely a complete random normed module is random reflexive iff the random norm of an arbitrary
almost surely bounded random linear functional on it is attainable on its random closed unit ball, but this paper shows that
the classical Banach-Alaoglu theorem and BBKS theorem do not hold universally for complete random normed modules unless they
possess extremely simple stratification structure, namely their supports are essentially purely μ-atomic. Combining the James
theorem and BBKS theorem in complete random normed modules leads directly to an interesting phenomenum: there exist many famous
classical propositions that are mutually equivalent in the case of Banach spaces, some of which remain to be mutually equivalent
in the context of arbitrary complete random normed modules, whereas the other of which are no longer equivalent to another
in the context of arbitrary complete random normed modules unless the random normed modules in question possess extremely
simple stratification structure. Such a phenomenum is, for the first time, discovered in the course of the development of
random metric theory. 相似文献
18.
The subgroups E(m,R) ⊗ E(n,R) ≤ H ≤ G = GL(mn,R) are studied under the assumption that the ring R is commutative and m, n ≥ 3. The group GL
m
⊗GL
n
is defined by equations, the normalizer of the group E(m,R) ⊗ E(n,R) is calculated, and with each intermediate subgroup H it is associated a uniquely determined lower level (A,B,C), where A,B,C are ideals in R such that mA,A
2 ≤ B ≤ A and nA,A
2 ≤ C ≤ A. The lower level specifies the largest elementary subgroup satisfying the condition E(m, n,R, A,B,C) ≤ H. The standard answer to this problem asserts that H is contained in the normalizer N
G
(E(m,n,R, A,B,C)). Bibliography: 46 titles. 相似文献
19.
We study the structure of bounded sets in the space L1{E} of absolutely integrable Lusin-measurable functions with values in a locally convex space E. The main idea is to extend the notion of property (B) of Pietsch, defined within the context of vector-valued sequences, to spaces of vector-valued functions. We prove that this extension, that at first sight looks more restrictive, coincides with the original property (B) for quasicomplete spaces. Then we show that when dealing with a locally convex space, property (B) provides the link to prove the equivalence between Radon–Nikodym property (the existence of a density function for certain vector measures) and the integral representation of continuous linear operators T: L1 → E, a fact well-known for Banach spaces. We also study the relationship between Radon–Nikodym property and the characterization of the dual of L1{E} as the space L∞{E′b}. 相似文献
20.
In [T2] it was shown that the classifying space of the stable mapping class groups after plus construction ℤ×BΓ+
∞ has an infinite loop space structure. This result and the tools developed in [BM] to analyse transfer maps, are used here
to show the following splitting theorem. Let Σ∞(ℂP
∞
+)∧
p
≃E
0∨...∨E
p-2
be the “Adams-splitting” of the p-completed suspension spectrum of ℂP
∞
+. Then for some infinite loop space W
p
,?(ℤ×BΓ+
∞)∧
p
≃Ω∞(E
0)×...×Ω∞(E
p-3
)×W
p
?where Ω∞
E
i
denotes the infinite loop space associated to the spectrum E
i
. The homology of Ω∞
E
i
is known, and as a corollary one obtains large families of torsion classes in the homology of the stable mapping class group.
This splitting also detects all the Miller-Morita-Mumford classes. Our results suggest a homotopy theoretic refinement of
the Mumford conjecture. The above p-adic splitting uses a certain infinite loop map?α∞:ℤ×BΓ+
∞?Ω∞ℂP
∞
-1?that induces an isomorphims in rational cohomology precisely if the Mumford conjecture is true. We suggest that α∞ might be a homotopy equivalence.
Oblatum 2-VIII-1999 & 28-III-2001?Published online: 18 June 2001 相似文献