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1.
Zhao Fang BAI Jin Chuan HOU 《数学学报(英文版)》2005,21(5):1167-1182
Let X be a (real or complex) Banach space with dimension greater than 2 and let B0(X) be the subspace of B(X) spanned by all nilpotent operators on X. We get a complete classification of surjective additive maps Ф on B0(X) which preserve nilpotent operators in both directions. In particular, if X is infinite-dimensional, we prove that Ф has the form either Ф(T) = cATA^-1 or Ф(T) = cAT'A^-1, where A is an invertible bounded linear or conjugate linear operator, c is a scalar, T' denotes the adjoint of T. As an application of these results, we show that every additive surjective map on B(X) preserving spectral radius has a similar form to the above with |c| = 1. 相似文献
2.
Haïkel Skhiri 《Acta Appl Math》2010,112(3):347-356
Let m(T) and q(T) be respectively the minimum and the surjectivity moduli of T∈ℬ(X), where ℬ(X) denotes the algebra of all bounded linear operators on a complex Banach space X. If there exists a semi-invertible but non-invertible operator in ℬ(X) then, given a surjective unital linear map φ: ℬ(X)⟶ℬ(X), we prove that m(T)=m(φ(T)) for all T∈ℬ(X), if and only if, q(T)=q(φ(T)) for all T∈ℬ(X), if and only if, there exists a bijective isometry U∈ℬ(X) such that φ(T)=UTU
−1 for all T∈ℬ(X). 相似文献
3.
Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: A → B satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; T ∈ A, then φ and ϕ are either of the form φ(T) = A
1
TA
2
−1 and ϕ(T) = A
2
TA
1
−1 for some bijective bounded linear operators A
1; A
2 of X onto Y, or of the form φ(T) = B
1
T*B
2
−1 and ϕ(T) = B
2
T*B
−1 for some bijective bounded linear operators B
1;B
2 of X* onto Y.
相似文献
4.
Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ -1,1,2,3, and A, B ∈ B(H),A-λB ∈I(H) ⇔ Φ(A) -λΦ(B) ∈I(H, then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT
-1 for all A ∈ B(H), or Φ(A) = TA*T
-1 for all A ∈ B(H); if, in addition, A-iB ∈I(H)⇔ Φ(A)-iΦ(B) ∈I(H), here i is the imaginary unit, then Φ is either an automorphism or an anti-automorphism. 相似文献
5.
Let p∈(0,1] and s≥[n(1/p−1)], where [n(1/p−1)] denotes the maximal integer no more than n(1/p−1). In this paper, the authors prove that a linear operator T extends to a bounded linear operator from the Hardy space H
p
(ℝ
n
) to some quasi-Banach space ℬ if and only if T maps all (p,2,s)-atoms into uniformly bounded elements of ℬ.
相似文献
6.
LetT(λ) be a bounded linear operator in a Banach spaceX for eachλ in the scalar fieldS. The characteristic value-vector problemT(λ)x = 0 with a normalization conditionφ x = 1, whereφ ε X
*, is formulated as a nonlinear problem inX xS:P(y) ≡ (T(λ)x, φ x - 1) = 0,y= (X, A). Newton's method and the Kantorovič theorem are applied. For this purpose, representations and criteria for existence
ofP′(y)−1 are obtained. The continuous dependence onT of characteristic values and vectors is investigated. A numerical example withT(λ) =A +λB +λ
2
C is presented.
Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462. 相似文献
7.
Let H be a Hilbert space and A be a standard *-subalgebra of B(H). We show that a bijective map Ф : A →A preserves the Lie-skew product AB - BA* if and only if there is a unitary or conjugate unitary operator U ∈A(H) such that Ф(A) = UAU* for all A ∈ A, that is, Фis a linear * -isomorphism or a conjugate linear *-isomorphism. 相似文献
8.
Let T and S be invertible measure preserving transformations of a probability measure space (X, ℬ, μ). We prove that if the group generated by T and S is nilpotent, then exists in L
2-norm for any u, v∈L
∞(X, ℬ, μ). We also show that for A∈ℬ with μ(A)>0 one has . By the way of contrast, we bring examples showing that if measure preserving transformations T, S generate a solvable group, then (i) the above limits do not have to exist; (ii) the double recurrence property fails, that
is, for some A∈ℬ, μ(A)>0, one may have μ(A∩T
-n
A∩S
-
n
A)=0 for all n∈ℕ. Finally, we show that when T and S generate a nilpotent group of class ≤c, in L
2(X) for all u, v∈L
∞(X) if and only if T×S is ergodic on X×X and the group generated by T
-1
S, T
-2
S
2,..., T
-c
S
c
acts ergodically on X.
Oblatum 19-V-2000 & 5-VII-2001?Published online: 12 October 2001 相似文献
9.
J. MALINEN O. NEVANLINNA V. TURUNEN Z. YUAN 《数学学报(英文版)》2007,23(4):745-748
Let T be a bounded linear operator in a Banach space, with σ(T)={1}. In 1983, Esterle-Berkani' s conjecture was proposed for the decay of differences (I - T) T^n as follows: Eitheror lim inf (n→∞(n+1)||(I-T)T^n||≥1/e or T = I. We prove this claim and discuss some of its consequences. 相似文献
10.
Aicke Hinrichs 《Archiv der Mathematik》1997,68(4):265-273
Let A
n
=(a
1,...,a
n) be a system of characters of a compact abelian group A
n
with normalized Haar measure μ and let T be a bounded linear operator from a Banach space X into a Banach space Y. The type norm τ(T|
A
n
) of T with respect to A
n
is the least constant c such that
for all x
1,..., x
n ∈ X. We investigate under which conditions on two systems A
n
and ℬ
n
of characters of compact abelian groups an inequality τ(T|ℬ
n) ≦ τ(T|A
n
) holds for all linear bounded operators T between Banach spaces. It turns out that this can be tested on a certain operator depending only on the system ℬ
n. Moreover, it is equivalent to strong algebraic relations between A
n
and ℬ
n as well as to relations between its distributions. In particular, for systems of trigonometric functions this inequality
for all linear bounded operators even implies equality for all linear bounded operators.
The author is supported by DFG grant PI 322/1-1. The content of this paper is part of the authors PhD-thesis written under
the supervision of A. Pietsch. 相似文献
11.
In this paper we consider a C*-subalgebra of the algebra of all bounded operators B(l2(X)) on the Hilbert space l2(X)) with one generating element T
φ induced by a mapping φ of a set X into itself. We prove that such a C* -algebra has an AF-subalgebra and establish commutativity conditions for the latter. We prove that a C* -algebra generated by a mapping produces a dynamic system such that the corresponding group of automorphisms is invariant
on elements of the AF- subalgebra. 相似文献
12.
Let L(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Given A ∈ L(H), we define the elementary operator Δ
A
: L(H) → L(H) by Δ
A
(X) = AXA − X. In this paper we study the class of operators A ∈ L(H) which have the following property: ATA = T implies AT*A = T* for all trace class operators T ∈ C
1(H). Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the
fact that the ultraweak closure of the range of Δ
A
is closed under taking adjoints. We give a characterization and some basic results concerning generalized quasi-adjoints
operators. 相似文献
13.
Osamu Hatori Takeshi Miura Rumi Shindo Hiroyuki Takagi 《Rendiconti del Circolo Matematico di Palermo》2010,59(2):161-183
Let $
A
$
A
and ℬ be unital semisimple commutative Banach algebras. It is shown that if surjections S,T: $
A
$
A
→ ℬ with S(1)=T(1)= 1 and α ∈ ℂ \ {0} satisfy r(S(a)T(b) − α)= r(ab− α) for all a,b ∈ $
A
$
A
, then S=T and S is a real algebra isomorphism, where r(a) is the spectral radius of a. Let I be a nonempty set, A and B be uniform algebras. Let ρ, τ: I → A and S,T: I → B be maps satisfying σ
π
(S(p)T(q)) ⊂ σ
π
(ρ(p) τ(q)) for all p,q ∈ I, where σ
π
(f) is the peripheral spectrum of f. Suppose that the ranges ρ(I), τ(I) ⊂ A and S(I),T(I) ⊂ B are closed under multiplication in a sense, and contain peaking functions “enough”. There exists a homeomorphism ϕ: Ch(B)→Ch(A) such that S(p)(y)= ρ(p)(ϕ(y)) and T(p)(y)= τ(p)(ϕ(y)) for every p ∈ I and y ∈ Ch(B), where Ch(A) is the Choquet boundary of A. 相似文献
14.
This paper considers the dual of anisotropic Sobolev spaces on any stratified groups 𝔾. For 0≤k<m and every linear bounded functional T on anisotropic Sobolev space W
m−k,p
(Ω) on Ω⊂𝔾, we derive a projection operator L from W
m,p
(Ω) to the collection 𝒫
k+1
of polynomials of degree less than k+1 such that T(X
I
(Lu))=T(X
I
u) for all uW
m,p
(Ω) and multi-index I with d(I)≤k. We then prove a general Poincaré inequality involving this operator L and the linear functional T. As applications, we often choose a linear functional T such that the associated L is zero and consequently we can prove Poincaré inequalities of special interests. In particular, we obtain Poincaré inequalities
for functions vanishing on tiny sets of positive Bessel capacity on stratified groups. Finally, we derive a Hedberg-Wolff
type characterization of measures belonging to the dual of the fractional anisotropic Sobolev spaces W
α,p
𝔾.
Received: 25 March 2002; in final form: 10 September 2002 /
Published online: 1 April 2003
Mathematics Subject Classification (1991): 46E35, 41A10, 22E25
The second author was supported partly by U.S NSF grant DMS99-70352 and the third author was supported partly by NNSF grant
of China. 相似文献
15.
Idealization of a decomposition theorem 总被引:1,自引:1,他引:0
In 1986, Tong [13] proved that a function f : (X,τ)→(Y,φ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A
I-sets and A
I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, φ) is continuous if and only if it is α-I-continuous and A
I-continuous.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
16.
In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x) := (φ1(x), . . . , φr(x))T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x) := (φn1 ew(x), . . . , φrn ew(x))T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally,... 相似文献
17.
Moshe Katz 《Israel Journal of Mathematics》1971,9(1):53-72
Let ℬ(m) be the set of all then-square (0–1) matrices containingm ones andn
2−m zeros, 0<m<n
2. The problem of finding the maximum ofs(A
2) over this set, wheres(A
2) is the sum of the entries ofA
2,A ∈ ℬ (m) is considered. This problem is solved in the particular casesm=n
2 −k
2 andm=k
2,k
2>(n
2/2).
This paper forms part of a thesis in partial fulfillment of the requirements for the degree of Doctor of Science at the Technion-Israel
Institute of Technology. The author wishes to thank Professor B. Schwarz and Dr. D. London for their help in the preparation
of this paper. 相似文献
18.
Masahiro Yasumoto 《manuscripta mathematica》1990,66(1):227-235
LetK be an algebraic number field of finite degree andf(X,T) a polynomial overK. For eachφ(X)∈Z[X], we denote byE(φ) the set of all integersa with φ
m
(a) =φ
n
(a) for somem≠n. In this paper, we give a condition for a polynomialφ(X)∈Z[X] to satisfy the following; If forn∈N, there existr∈K anda∈Z−E(φ) such thatf r, φ
m
(a)=0, then there exists a rational functiong(X) overK andk∈N such thatf(g(T)), φ
k
(T))=0 . 相似文献
19.
Horst R. Thieme 《Journal of Evolution Equations》2008,8(2):283-305
If T = {T (t); t ≥ 0} is a strongly continuous family of bounded linear operators between two Banach spaces X and Y and f ∈ L
1(0, b, X), the convolution of T with f is defined by . It is shown that T * f is continuously differentiable for all f ∈ C(0, b, X) if and only if T is of bounded semi-variation on [0, b]. Further T * f is continuously differentiable for all f ∈ L
p
(0, b, X) (1 ≤ p < ∞) if and only if T is of bounded semi-p-variation on [0, b] and T(0) = 0. If T is an integrated semigroup with generator A, these respective conditions are necessary and sufficient for the Cauchy problem u′ = Au + f, u(0) = 0, to have integral (or mild) solutions for all f in the respective function vector spaces. A converse is proved to a well-known result by Da Prato and Sinestrari: the generator
A of an integrated semigroup is a Hille-Yosida operator if, for some b > 0, the Cauchy problem has integral solutions for all f ∈ L
1(0, b, X). Integrated semigroups of bounded semi-p-variation are preserved under bounded additive perturbations of their generators and under commutative sums of generators
if one of them generates a C
0-semigroup.
Günter Lumer in memoriam 相似文献