共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
Marcus Carlsson 《Integral Equations and Operator Theory》2008,61(4):593-598
In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M
z
on a Hilbert space -valued analytic functions, where M
z
denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s
theorem.
In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works
for Banach space operators.
相似文献
3.
Jie Miao 《Integral Equations and Operator Theory》2007,59(1):53-65
We give a necessary and sufficient condition for Hankel operators Hf on the harmonic Bergman space of the unit ball to be in the Schatten p-class for 2 ≤ p < ∞. A special case when symbol f is a harmonic function is also considered. 相似文献
4.
V. A. Khatskevich M. I. Ostrovskii V. S. Shulman 《Integral Equations and Operator Theory》2007,59(1):19-34
Properties of sets of solutions to inequalities of the form
are studied, where A, B, C are bounded Hilbert space operators, A and C are self-adjoint. Properties under consideration: closeness and interior points in standard operator topologies, convexity,
non-emptiness. 相似文献
5.
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
6.
Dr. Mohammed Hichem Mortad 《Integral Equations and Operator Theory》2009,64(3):399-408
We give a spectral analysis of some unbounded normal product HK of two self-adjoint operators H and K (which appeared in [7]) and we say why it is not self-adjoint even if the spectrum of one of the operators is sufficiently
“asymmetric”. Then, we investigate the self-adjointness of KH (given it is normal) for arbitrary self-adjoint H and K by giving a counterexample and some positive results and hence finishing off with the whole question of normal products of
self-adjoint operators (appearing in [1, 7, 12]).
The author was supported in part by CNEPRU: B01820070020 (Ministry of Higher Education, Algeria). 相似文献
7.
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
8.
Oscar F. Bandtlow 《Integral Equations and Operator Theory》2008,61(1):21-43
For a, α > 0 let E(a, α) be the set of all compact operators A on a separable Hilbert space such that s
n
(A) = O(exp(-anα)), where s
n
(A) denotes the n-th singular number of A. We provide upper bounds for the norm of the resolvent (zI − A)−1 of A in terms of a quantity describing the departure from normality of A and the distance of z to the spectrum of A. As a consequence we obtain upper bounds for the Hausdorff distance of the spectra of two operators in E(a, α).
相似文献
9.
It is well known that there are classes of test functions such that a Hankel operator is bounded if and only if it is bounded
on those functions. Criteria are derived which determine whether a Hankel operator is compact or belongs to a particular Schatten
class, in terms of its action on those test functions. 相似文献
10.
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
11.
Kyunguk Na 《Integral Equations and Operator Theory》2009,64(3):409-428
We study characterizations of arbitrary positive Toeplitz operators of Schatten (or Schatten-Herz) type in terms of averaging
functions and Berezin transforms of symbol functions on the ball of pluriharmonic Bergman space.
This work was supported by a Hanshin University Research Grant. 相似文献
12.
Let be a multiplicative semigroup of positive operators on a Banach lattice E such that every is ideal-triangularizable, i.e., there is a maximal chain of closed subspaces of E that consists of closed ideals invariant under S. We consider the question under which conditions the whole semigroup is simultaneously ideal-triangularizable. In particular, we extend a recent result of G. MacDonald and H. Radjavi. We also
introduce a class of positive operators that contains all positive abstract integral operators when E is Dedekind complete.
相似文献
13.
On The Extended Eigenvalues of Some Volterra Operators 总被引:2,自引:0,他引:2
Srdjan Petrovic 《Integral Equations and Operator Theory》2007,57(4):593-598
We show that a large class of compact quasinilpotent operators has extended eigenvalues. As a consequence, if V is such an operator, then the associated spectral algebra
contains its commutant {V}' as a proper subalgebra. 相似文献
14.
Let X be a complex Banach space, and let
be the space of bounded operators on X. Given
and x ∈ X, denote by σT (x) the local spectrum of T at x.
We prove that if
is an additive map such that
then Φ (T) = T for all
We also investigate several extensions of this result to the case of
where
The proof is based on elementary considerations in local spectral theory, together with the following local identity principle:
given
and x ∈X, if σS+R (x) = σT+R (x) for all rank one operators
then Sx = Tx . 相似文献
15.
Elena Litsyn 《Integral Equations and Operator Theory》2007,58(2):239-253
The new definition of Volterra operator introduced in [5] allows specification of the classical theory of linear equations
in Banach spaces to equations with such operators. Here we specially address relations between properties of the given linear
equation with Volterra operator and properties of its conjugate. As well we treat the theory of Noetherian and Fredholm equations. 相似文献
16.
For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator
is bounded on
where
is the open unit ball in
and dvt (z) = (1 − |z| 2) t dv (z) with dv being volume measure on
The characterization remains the same if we replace (1 − 〈z, w 〉) c in the integral kernel above by its modulus |1 − 〈z, w〉| c. 相似文献
17.
We introduce the notion of spectralizable operators. A closed operator A in a Hilbert space is called spectralizable if there exists a non-constant polynomial p such that the operator p(A) is a scalar spectral operator in the sense of Dunford. We show that such operators belongs to the class of generalized spectral
operators and give some examples where spectralizable operators occur naturally.
Vladimir Strauss gratefully acknowledges support by DFG, Grant No. TR 903/3-1. 相似文献
18.
19.
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
20.
Fritz Gesztesy Mark Malamud Marius Mitrea Serguei Naboko 《Integral Equations and Operator Theory》2009,64(1):83-113
We study generalized polar decompositions of densely defined closed linear operators in Hilbert spaces and provide some applications
to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators.
Based upon work partially supported by the US National Science Foundation under Grant Nos. DMS-0400639 and FRG-0456306, and
the Austrian Science Fund (FWF) under Grant No. Y330. 相似文献