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1.
Multiplication operators in weighted Banach (and locally convex) spaces of functions holomorphic in the unit disc are well
known. In this note we investigate the connection between power boundedness, mean ergodicity and uniform mean ergodicity of
such operators.
Received: 13 October 2008, Revised: 18 November 2008 相似文献
2.
Let A
0, ... , A
n−1 be operators on a separable complex Hilbert space , and let α0,..., α
n−1 be positive real numbers such that 1. We prove that for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequality holds for 0 < p ≤ 2. Moreover, we prove that if ω0,..., ω
n−1 are the n roots of unity with ω
j
= e
2πij/n
, 0 ≤ j ≤ n − 1, then for every unitarily invariant norm,
for 2 ≤ p < ∞, and the reverse inequalities hold for 0 < p ≤ 2. These inequalities, which involve n-tuples of operators, lead to natural generalizations and refinements of some of the classical Clarkson inequalities in the
Schatten p-norms. Extensions of these inequalities to certain convex and concave functions, including the power functions, are olso
optained.
相似文献
3.
Muneo Chō Mariko Giga Tadasi Huruya Takeaki Yamazaki 《Integral Equations and Operator Theory》2007,57(3):303-308
Let
be an invertible class A operator such that
. Then we show that
, where gT is the principal function of T. Moreover, we show that if T is pure, then
. 相似文献
4.
Anders Olofsson 《Integral Equations and Operator Theory》2007,58(4):503-549
We study an operator-valued Berezin transform corresponding to certain standard weighted Bergman spaces of square integrable
analytic functions in the unit disc. The study of this operator-valued Berezin transform relates in a natural way to the study
of the class of n-hypercontractions on Hilbert space introduced by Agler. To an n-hypercontraction
we associate a positive
-valued operator measure dω
n, T
supported on the closed unit disc
in a way that generalizes the above notion of operator-valued Berezin transform. This construction of positive operator measures
dω
n, T
gives a natural functional calculus for the class of n-hypercontractions. We revisit also the operator model theory for the class of n-hypercontractions. The new results here concern certain canonical features of the theory. The operator model theory for the
class of n-hypercontractions gives information about the structure of the positive operator measures dω
n, T
. 相似文献
5.
In this paper, we introduce Xia spectra of n-tuples of operators satisfying |T
2| ≥ U|T
2|U* for the polar decomposition of T = U|T| and we extend Putnam’s inequality to these tuples [7].
This research is partially supported by Grant-in-Aid Research No.17540176. 相似文献
6.
Mohamed Bendaoud 《Archiv der Mathematik》2009,92(3):257-265
Let be a complex Hilbert space and let be the algebra of all bounded linear operators on . We characterize additive maps from onto itself preserving different spectral quantities such as the minimum modulus, the surjectivity modulus, and the maximum
modulus of operators.
Received: 15 July 2008 相似文献
7.
Andrzej Kryczka 《Integral Equations and Operator Theory》2008,61(4):559-572
We introduce the arithmetic separation of a sequence—a geometric characteristic for bounded sequences in a Banach space which
describes the Banach-Saks property. We define an operator seminorm vanishing for operators with the Banach-Saks property.
We prove quantitative stability of the seminorm for a class of operators acting between l
p
-sums of Banach spaces. We show logarithmically convex-type estimates of the seminorm for operators interpolated by the real
method of Lions and Peetre.
相似文献
8.
We define and study the Fock space associated with the spherical mean operator. Next, we establish some results for the Segal-Bergmann
transform for this space. Lastly, we prove some properties concerning Toeplitz operators on this space.
Received: May 11, 2007. Revised: May 20, 2008. Accepted: May 23, 2008. 相似文献
9.
The standard correspondence between the normal subgroups of the group G and some ideals of the group algebra FG is described. There is the problem of what we can say (or even prove) about a two-sided ideal of that does not contain any element of the form 1 − g ≠ 0, g ∈G of the standard basis of the augmentation ideal of . The main part of the argument of [2] yields the insight that, for such an ideal I there exists an expansion such that the ideal J of spanned by I contains an element 1 − h, h ∈ H \ G. Using the ideas of [2], we construct -thick groups H such that for every ideal J ≠ (0) of there are elements 1 − h ≠ 0 in J. This construction allows many variations. Examples of simple -thick groups were pointed out in [2]. A natural class of (in general non-simple) -full groups are the normal sections of the groups
(Here, Fin(M) is the subgroup of all finitary permutations of M.)
Received: July 2007 相似文献
10.
We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space with the resolvent norm
that is constant in a neighbourhood of zero.
相似文献
11.
M. M. Popov 《Archiv der Mathematik》2008,90(6):537-544
The well known Daugavet property for the space L
1 means that || I + K || = 1+ || K || for any weakly compact operator K : L
1 → L
1, where I is the identity operator in L
1. We generalize this theorem to the case when we consider an into isomorphism J : L
1 → L
1 instead of I and a narrow operator T. Our main result states that , where d = || J|| || J
−1||. We also give an example which shows that this estimate is exact.
Received: 21 August 2007 相似文献
12.
Let A be a unital C*-algebra with non-zero socle (soc(A)). We introduce the essential conorm of an element a in A (denoted by γ
e
(a)), as the conorm of the element π(a), where π denotes the canonical projection of A onto . It is established that for every von Neumann regular element , γ
e
(a) = max . We characterize the continuity points of the conorm and essential conorm for extremally rich C*-algebras. Some formulae for the distance from zero to the generalized spectrum and Atkinson spectrum are also obtained.
Authors partially supported by I+D MEC projects no. MTM2005-02541 and MTM2007-65959, and Junta de Andalucía grants FQM0199
and FQM1215. 相似文献
13.
Wolfgang Hackenbroch 《Archiv der Mathematik》2009,92(5):485-492
In a Hilbert space context, we propose a rather general notion of “random operators” which allows for taking stochastic limits.
After establishing a connection with measurable fields of closed operators, we may speak of a spectral theory for symmetric
random operators.
Received: 18 December 2008 相似文献
14.
15.
The classical Krein-Naimark formula establishes a one-to-one correspondence between the generalized resolvents of a closed
symmetric operator in a Hilbert space and the class of Nevanlinna families in a parameter space. Recently it was shown by
V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo that these parameter families can be interpreted as so-called Weyl
families of boundary relations, and a new proof of the Krein-Naimark formula in the Hilbert space setting was given with the
help of a coupling method. The main objective of this paper is to adapt the notion of boundary relations and their Weyl families
to the Krein space case and to prove some variants of the Krein-Naimark formula in an indefinite setting.
相似文献
16.
Pascal Lefèvre 《Integral Equations and Operator Theory》2009,63(4):557-569
We compute the essential norm of a composition operator relatively to the class of Dunford-Pettis operators or weakly compact
operators, on some uniform algebras of analytic functions. Even in the context of H∞ (resp. the disk algebra), this is new, as well for the polydisk algebras and the polyball algebras. This is a consequence
of a general study of weighted composition operators.
相似文献
17.
S. Shkarin 《Integral Equations and Operator Theory》2009,64(1):115-136
It is shown that if 1 < p < ∞ and X is a subspace or a quotient of an ℓp-direct sum of finite dimensional Banach spaces, then for any compact operator T on X such that ∥I + T∥ > 1, the operator I + T attains its norm. A reflexive Banach space X and a bounded rank one operator T on X are constructed such that ∥I + T∥ > 1 and I + T does not attain its norm.
The author would like to thank E. Shargorodsky for his interest and comments. 相似文献
18.
B. P. Duggal 《Integral Equations and Operator Theory》2009,63(1):17-28
A Banach space operator T ∈ B(χ) is polaroid if points λ ∈ iso σ(T) are poles of the resolvent of T. Let denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower
semi–Fredholm spectrum of T. For A, B and C ∈ B(χ), let M
C
denote the operator matrix . If A is polaroid on , M
0 satisfies Weyl’s theorem, and A and B satisfy either of the hypotheses (i) A has SVEP at points and B has SVEP at points , or, (ii) both A and A* have SVEP at points , or, (iii) A* has SVEP at points and B
* has SVEP at points , then . Here the hypothesis that λ ∈ π0(M
C
) are poles of the resolvent of A can not be replaced by the hypothesis are poles of the resolvent of A.
For an operator , let . We prove that if A* and B* have SVEP, A is polaroid on π
a
0(M
C) and B is polaroid on π
a
0(B), then .
相似文献
19.
Bebe Prunaru 《Integral Equations and Operator Theory》2008,61(1):121-145
In this paper we establish a connection between the approximate factorization property appearing in the theory of dual algebras
and the spectral inclusion property for a class of Toeplitz operators on Hilbert spaces of vector valued square integrable
functions. As an application, it follows that a wide range of dual algebras of subnormal Toeplitz operators on various Hardy
spaces associated to function algebras have property (A
1(1)). It is also proved that the dual algebra generated by a spherical isometry (with a possibly infinite number of components)
has the same property. One particular application is given to the existence of unimodular functions sitting in cyclic invariant
subspaces of weak* Dirichlet algebras. Moreover, by this method we provide a unified approach to several Toeplitz spectral
inclusion theorems.
Research partially supported by grant CNCSIS GR202/2006 (cod 813). 相似文献