共查询到20条相似文献,搜索用时 31 毫秒
1.
Hyoung Joon Kim 《Integral Equations and Operator Theory》2008,61(1):103-120
In this paper we consider the hyperinvariant subspace problem for quasinilpotent operators. Let denote the class of quasinilpotent quasiaffinities Q in such that Q
*
Q has an infinite dimensional reducing subspace M with Q
*
Q|
M
compact. It was known that if every quasinilpotent operator in has a nontrivial hyperinvariant subspace, then every quasinilpotent operator has a nontrivial hyperinvariant subspace. Thus
it suffices to solve the hyperinvariant subspace problem for elements in . The purpose of this paper is to provide sufficient conditions for elements in to have nontrivial hyperinvariant subspaces. We also introduce the notion of “stability” of extremal vectors to give partial
solutions to the hyperinvariant subspace problem.
相似文献
2.
Niels Grønbæk 《Proceedings Mathematical Sciences》2008,118(2):235-243
Let be a Banach algebra and let X be a Banach -bimodule. In studying (,X) it is often useful to extend a given derivation D: → X to a Banach algebra containing as an ideal, thereby exploiting (or establishing) hereditary properties. This is usually done using (bounded/unbounded) approximate
identities to obtain the extension as a limit of operators b ↦ D(ba) − b.D(a), a ε in an appropriate operator topology, the main point in the proof being to show that the limit map is in fact a derivation.
In this paper we make clear which part of this approach is analytic and which algebraic by presenting an algebraic scheme
that gives derivations in all situations at the cost of enlarging the module. We use our construction to give improvements
and shorter proofs of some results from the literature and to give a necessary and sufficient condition that biprojectivity
and biflatness is inherited to ideals. 相似文献
3.
Camil Muscalu 《Journal of Geometric Analysis》1999,9(4):683-691
If N ∈ ℕ, 0 < p ≤ 1, and(Xk)
k=1
N
are r.i.p-spaces, it is shown that there is C(= C(p, N)) > 0, such that for every ƒ ∈ ∩
k=1
N
Xk, there exists
with
, for every 1 ≤ k ≤ N. Also, if ⊓ is a convex polygon in ℝ2, it is proved that the N-tuple (H(X1),…, H(Xn)) is K⊓-closed with respect to (X1,…, XN) in the sense of Pisier. Everything follows from Theorem 2.1, which is a general analytic partition of unity type result. 相似文献
4.
John W. Snow 《Algebra Universalis》2008,58(1):59-71
We prove that if is a finite algebra which satisfies a nontrivial idempotent Mal’cev condition, and if Con contains a copy of an order polynomially complete lattice other than , , or Con, then Con is not hereditary.
Received March 7, 2006; accepted in final form December 5, 2006. 相似文献
5.
Let X be a Banach space. We give characterizations of when is a u-ideal in for every Banach space Y in terms of nets of finite rank operators approximating weakly compact operators. Similar characterizations are given for
the cases when is a u-ideal in for every Banach space Y, when is a u-ideal in for every Banach space Y, and when is a u-ideal in for every Banach space Y. 相似文献
6.
Pier Domenico Lamberti Massimo Lanza de Cristoforis 《Mediterranean Journal of Mathematics》2007,4(4):435-449
Let Ω be an open connected subset of for which the imbedding of the Sobolev space W
1,2(Ω) into the space L
2(Ω) is compact. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset (Ω) of , where is a Lipschitz continuous homeomorphism of Ω onto (Ω). Then we prove a result of real analytic dependence for symmetric functions of the eigenvalues upon variation of .
This paper represents an extension of a part of the work performed by P.D. Lamberti in his PhD Thesis at the University of
Padova under the guidance of M. Lanza de Cristoforis. 相似文献
7.
A set of positive integers is a perfect difference set if every nonzero integer has a unique representation as the difference of two elements of . We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set such that
.
Also we prove that there exists a perfect difference set
such that
A(x)/≥ 1/.
The work of J. C. was supported by Grant MTM 2005-04730 of MYCIT (Spain).
The work of M. B. N. was supported in part by grants from the NSA Mathematical Sciences Program and the PSC-CUNY Research
Award Program. 相似文献
8.
We consider the 2-D Keller-Segel system (KS) for γ > 0. We first construct a mild solution of (KS) for every . The local existence time is characterized for with 1 < q
* < 2. Next, we prove the finite time blow-up of strong solution under the assumption and , where g(s) is an increasing function of s > 1 with an explicit representation. As an application of our mild solutions, an exact blow-up rate near the maximal existence
time is obtained.
相似文献
9.
JianMing Chang 《中国科学A辑(英文版)》2009,52(8):1717-1722
Let be a family of meromorphic functions in a plane domain D, and a and b be finite non-zero complex values such that . If for and , then is normal. We also construct a non-normal family of meromorphic functions in the unit disk Δ={|z|<1} such that for every and in Δ, where m is a given positive integer. This answers Problem 5.1 in the works of Gu, Pang and Fang.
This work was supported by National Natural Science Foundation of China (Grant Nos. 10671093, 10871094) and the Natural Science
Foundation of Universities of Jiangsu Province of China (Grant No. 08KJB110001), the Qing Lan Project of Jiangsu, China and
the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry 相似文献
10.
In this paper we mainly study the derivations for even part of the finite-dimensional odd Hamiltonian superalgebra HO over a field of prime characteristic. We first give the generating set of the even part g of HO. Then we compute the derivations from g into the even part m of the generalized Witt superalgebra. Finally, we determine the derivation algebra and outer derivation algebra of and the dimension formulas. In particular, the first cohomology groups H^1(g;m) and H^1(g;g) are determined. 相似文献
11.
We study the set of infinitely differentiable periodic functions in terms of generalized -derivatives defined by a pair of sequences ψ
1 and ψ
2. It is shown that every function ƒ from the set has at least one derivative whose parameters ψ
1 and ψ
2 decrease faster than any power function and, at the same time, for any function ƒ ∈ different from a trigonometric polynomial, there exists a pair ψ whose parameters ψ
1 and ψ
2 have the same rate of decrease and for which the -derivative no longer exists.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 10, pp. 1399–1409, October, 2007. 相似文献
12.
Let G be an additive subgroup of a normed space X. We say that a point is weakly separated (resp. -separated) from G if it can be separated from G by a continuous character (resp. by a continuous positive definite function). Let T : X → Y be a continuous linear operator. Consider the following conditions:
(ws) if , then x is weakly separated from G;
(ps) if , then x is -separated from G;
(wp) if Tx is -separated from T(G), then x is weakly separated from G.
By (resp. , ) we denote the class of operators T : X → Y which satisfy (ws) (resp. (ps), (wp)) for all and all subgroups G of X. The paper is an attempt to describe the above classes of operators for various Banach spaces X, Y. It is proved that if X, Y are Hilbert spaces, then is the class of Hilbert-Schmidt operators. It is also shown that if T is a Hilbert-to-Banach space operator with finite ℓ-norm, then .
相似文献
13.
By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria and study the
asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation
, on a time scale . The results improve some oscillation results for neutral delay dynamic equations and in the special case when = ℝ our results cover and improve the oscillation results for second-order neutral delay differential equations established
by Li and Liu [Canad. J. Math., 48 (1996), 871–886]. When = ℕ, our results cover and improve the oscillation results for second order neutral delay difference equations established
by Li and Yeh [Comp. Math. Appl., 36 (1998), 123–132]. When =hℕ, = {t: t = q
k
, k ∈ ℕ, q > 1}, = ℕ2 = {t
2: t ∈ ℕ}, = = {t
n
= Σ
k=1
n
, n ∈ ℕ0}, ={t
2: t ∈ ℕ}, = {√n: n ∈ ℕ0} and ={: n ∈ ℕ0} our results are essentially new. Some examples illustrating our main results are given.
相似文献
14.
We prove Tolokonnikov’s Lemma and the inner-outer factorization for the real Hardy space
, the space of bounded holomorphic (possibly operator-valued) functions on the unit disc all of whose matrix-entries (with
respect to fixed orthonormal bases) are functions having real Fourier coefficients, or equivalently, each matrix entry f satisfies
for all z ∈
.
Tolokonnikov’s Lemma for
means that if f is left-invertible, then f can be completed to an isomorphism; that is, there exists an F, invertible in
, such that F = [ f f
c
] for some f
c
in
. In control theory, Tolokonnikov’s Lemma implies that if a function has a right coprime factorization over
, then it has a doubly coprime factorization in
. We prove the lemma for the real disc algebra
as well. In particular,
and
are Hermite rings.
The work of the first author was supported by Magnus Ehrnrooth Foundation.
Received: December 5, 2006. Revised: February 4, 2007. 相似文献
15.
Friedrich Haslinger 《Czechoslovak Mathematical Journal》2008,58(4):1247-1256
We prove that compactness of the canonical solution operator to restricted to (0, 1)-forms with holomorphic coefficients is equivalent to compactness of the commutator
defined on the whole L
(0,1)2(Ω), where is the multiplication by and is the orthogonal projection of L
(0,1)2(Ω) to the subspace of (0, 1) forms with holomorphic coefficients. Further we derive a formula for the -Neumann operator restricted to (0, 1) forms with holomorphic coefficients expressed by commutators of the Bergman projection
and the multiplications operators by z and .
Partially supported by the FWF grant P19147-N13. 相似文献
16.
S. Norvidas 《Lithuanian Mathematical Journal》2008,48(1):92-99
Let
be a complex unital Banach algebra. An element a ∈
is said to be Hermitian if ‖exp(ita)‖ = 1 for all t ∈ ℝ. In the case of the algebra of bounded linear operators in a Hilbert space, this Hermitian property agrees with the ordinary
self-adjointness. If a ∈
is Hermitian, then ‖a‖ = |a|, where |a| denotes the spectral radius of a. A function F: ℝ → ℂ is called a universal symbol if ‖F(a)‖ = | F(a)| for every
and all Hermitian a ∈
. We characterize universal symbols in terms of positive-definite functions. 相似文献
17.
Laurent Bartholdi 《Israel Journal of Mathematics》2008,168(1):153-165
We study amenability of algebras and modules (based on the notion of almost-invariant finite-dimensional subspace), and apply
it to algebras associated with finitely generated groups.
We show that a group G is amenable if and only if its group ring
G is amenable for some (and therefore for any) field .
Similarly, a G-set X is amenable if and only if its span
X is amenable as a
G-module for some (and therefore for any) field . 相似文献
18.
Michael R. Darnel 《Algebra Universalis》2007,57(3):273-290
It is well known that the quasitorsion class of archimedean -groups is the class of -groups G such that every closed convex -subgroup is a polar, and it is also well known that the class of -groups G such that every convex -subgroup is a polar is a torsion class. By defining a selection on -groups, these two results are generalized to show, whenever and are selections on -groups, the class of -groups G such that is a radical class. Three selections in particular — all convex -subgroups, all polars, and all closed convex -subgroups — and the radical classes determined by them are studied in some detail.
Received March 7, 2006; accepted in final form August 29, 2006. 相似文献
19.
V. D. Lyakhovsky 《Journal of Mathematical Sciences》2008,151(2):2907-2923
New solutions of twist equations for the universal enveloping algebras U (An−1) are found. These solutions can be represented as products of full chains of extended Jordanian twists Abelian factors (“rotations”) , and sets of quasi-Jordanian twists . The latter are generalizations of Jordanian twists (with carrier b2) for special deformed extensions of the Hopf algebra U (b2). The carrier subalgebra for the composition is a nonminimal parabolic subalgebra in A
n−1 such that . The parabolic twisting elements are obtained in an explicit form. Details of the construction are illustrated by considering the examples n = 4 and n = 11.
Bibliography: 21 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 187–213. 相似文献
20.
Let
be a (not necessarily semi-finite) σ-finite von Neumann algebra. We prove that there exists a finite von Neumann algebra
so that for every 1 < p < 2, the Haagerup L
p
-space associated with
embeds isomorphically into
. We also provide a proof of the following non-commutative generalization of a classical result of Rosenthal: if
is a semi-finite von Neumann algebra then every reflexive subspace of
embeds isomorphically into L
r
(
) for some r > 1.
Dedicated to Professor H. P. Rosenthal on the occasion of his sixty-fifth birthday
Research partially supported by NSF grant DMS-0456781. 相似文献