共查询到20条相似文献,搜索用时 31 毫秒
1.
V. Kostrykin K. A. Makarov A. K. Motovilov 《Integral Equations and Operator Theory》2005,51(1):121-140
Let A and C be self-adjoint operators such that the spectrum of A lies in a gap of the spectrum of C and let d > 0 be the distance between the spectra of A and C. Under these assumptions we prove that the best possible value of the constant c in the condition
guaranteeing the existence of a (bounded) solution to the operator Riccati equation XA–CX+XBX = B* is equal to
We also prove an extension of the Davis-Kahan tan theorem and provide a sharp estimate for the norm of the solution to the Riccati equation. If C is bounded, we prove, in addition, that the solution X is a strict contraction if B satisfies the condition
and that this condition is optimal. 相似文献
2.
Bhagwati Prashad Duggal Slavisa V. Djordjević 《Mediterranean Journal of Mathematics》2005,2(4):395-406
It is known that if
and
are Banach space operators with the single-valued extension property, SVEP, then the matrix operator
has SVEP for every operator
and hence obeys Browder’s theorem. This paper considers conditions on operators A, B, and M0 ensuring Weyls theorem for operators MC. 相似文献
3.
Let B(H) denote the algebra of operators on a complex Hilbert
space H, and let U denote the class of operators
which satisfy
the absolute value condition
.
It is proved that if
is a
contraction, then either A has a nontrivial invariant subspace or A is a proper
contraction and the nonnegative operator
is strongly stable. A Putnam-Fuglede type commutativity theorem is proved for contractions A in
,
and it is shown that if normal subspaces of
. It is proved that if
are reducing, then every compact operator in the intersection of the weak closure of the range of the
derivation
with the commutant of A* is quasinilpotent. 相似文献
4.
For an invariant subspace I of the Bergman space
on the unit disk D, the associated inner space I zI has been known to have nice properties K. Zhu has recently given, in terms of kernels of Hankel operators, several characterizations for an inner space to be maximal. We show that maximality of inner spaces can be understood alternatively by use of the adjoint operator of the Bergman shift operator on
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5.
If E is a separable symmetric sequence space with trivial Boyd indices and
is the corresponding ideal of compact operators, then there exists a C1-function fE, a self-adjoint element
and a densely defined closed symmetric derivation δ on
such that
, but
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6.
Ovidiu Furdui 《Integral Equations and Operator Theory》2008,60(4):469-483
In this paper we consider the space where dv
s
is the Gaussian probability measure. We give necessary and sufficient conditions for the boundedness of some classes of integral
operators on these spaces. These operators are generalizations of the classical Bergman projection operator induced by kernel
function of Fock spaces over .
相似文献
7.
Pei Yuan Wu 《Integral Equations and Operator Theory》2006,56(4):559-569
Let A be a bounded linear operator on a complex separable Hilbert space H. We show that A is a C0(N) contraction if and only if
, where U is a singular unitary operator with multiplicity
and x1, . . . , xd are orthonormal vectors satisfying
. For a C0(N) contraction, this gives a complete characterization of its polar decompositions with unitary factors. 相似文献
8.
Henrik Petersson 《Integral Equations and Operator Theory》2007,57(3):413-423
We prove that for any weighted backward shift B = Bw on an infinite dimensional separable Hilbert space H whose weight sequence w = (wn) satisfies
, the conjugate operator
is hypercyclic on the space S(H) of self-adjoint operators on H provided with the topology of uniform convergence on compact sets. That is, there exists an
such that
is dense in S(H). We generalize the result to more general conjugate maps
, and establish similar results for other operator classes in the algebra B(H) of bounded operators, such as the ideals K(H) and N(H) of compact and nuclear operators respectively. 相似文献
9.
Let E and F be vector lattices and
the ordered space of all regular operators, which turns out to be a (Dedekind complete) vector lattice if F is Dedekind complete. We show that every lattice isomorphism from E onto F is a finite element in
, and that if E is an AL-space and F is a Dedekind complete AM-space with an order unit, then each regular operator is a finite element in
. We also investigate the finiteness of finite rank operators in Banach lattices. In particular, we give necessary and sufficient
conditions for rank one operators to be finite elements in the vector lattice
.
A half year stay at the Technical University of Dresden was supported by China Scholarship Council. 相似文献
10.
The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. 相似文献
11.
The strongly irreducible operators in nest algebras 总被引:2,自引:0,他引:2
An operatorT on
is called strongly irreducible ifT does not commute with any nontrivial idempotent operator. In this paper, we first show that each nest algebra (
) has strongly irreducible operators. Secondly, we obtain a characterization of operators which can be uniquely written as a direct sum of finitely many strongly irreducible operators. Finally, we characterize the strongly irreducibility of operators in a nest algebra (
).This project was partially supported by National Natural Science Foundation of China. 相似文献
12.
Nathan S. Feldman 《Integral Equations and Operator Theory》2000,37(4):402-422
We study pure subnormal operators whose self-commutators have zero as an eigenvalue. We show that various questions in this are closely related to questions involving approximation by functions satisfying
and to the study ofgeneralized quadrature domains.First some general results are given that apply to all subnormal operators within this class; then we consider characterizing the analytic Toeplitz operators, the Hardy operators and cyclic subnormal operators whose self-commutators have zero as an eigenvalue. 相似文献
13.
We study sums of bisectorial operators on a Banach space X and show that interpolation spaces between X and D(A) (resp. D(B)) are maximal regularity spaces for the problem Ay + By = x in X. This is applied to the study of regularity properties of the evolution equation u′ + Au = f on
for
or
and the evolution equation u′ + Au = f on [0, 2π] with periodic boundary condition u(0) = u(2π) in
or
相似文献
14.
Victor I. Lomonosov Heydar Radjavi Vladimir G. Troitsky 《Integral Equations and Operator Theory》2008,60(3):405-418
An algebra of operators on a Banach space X is said to be transitive if X has no nontrivial closed subspaces invariant under every member of the algebra. In this paper we investigate a number of
conditions which guarantee that a transitive algebra of operators is “large” in various senses. Among these are the conditions
of algebras being localizing or sesquitransitive. An algebra is localizing if there exists a closed ball B ∌ 0 such that for every sequence (x
n
) in B there exists a subsequence and a bounded sequence (A
k
) in the algebra such that converges to a non-zero vector. An algebra is sesquitransitive if for every non-zero z ∈ X there exists C > 0 such that for every x linearly independent of z, for every non-zero y ∈ X, and every there exists A in the algebra such that and ||Az|| ≤ C||z||. We give an algebraic version of this definition as well, and extend Jacobson’s density theorem to algebraically sesquitransitive
rings.
The second and the third authors were supported by NSERC. 相似文献
15.
Ghislain Vaillant 《Integral Equations and Operator Theory》1995,22(3):339-351
In this note we show that a separable C*-algebra is nuclear and has a quasidiagonal extension by
(the ideal of compact operators on an infinite-dimensional separable Hilbert space) if and only if it is anuclear finite algebra (NF-algebra) in the sense of Blackadar and Kirchberg, and deduce that every nuclear C*-subalgebra of aNF-algebra isNF. We show that strongNF-algebras satisfy a Følner type condition. 相似文献
16.
Markus Haase 《Mathematische Annalen》2009,345(2):245-265
Let –iA be the generator of a C
0-group on a Banach space X and ω > θ(U), the group type of U. We prove a transference principle that allows to estimate in terms of the -Fourier multiplier norm of . If X is a Hilbert space this yields new proofs of important results of McIntosh and Boyadzhiev–de Laubenfels. If X is a UMD space, one obtains a bounded -calculus of A on horizontal strips. Related results for sectorial and parabola-type operators follow. Finally it is proved that each generator
of a cosine function on a UMD space has bounded -calculus on sectors. 相似文献
17.
In this paper we show that the theory of Hankel operators in the torus
d
, ford>1, presents striking differences with that on the circle
, starting with bounded Hankel operators with no bounded symbols. Such differences are circumvented here by replacing the space of symbolsL
(
) by BMOr(
d
), a subspace of product BMO, and the singular numbers of Hankel operators by so-called sigma numbers. This leads to versions of the Nehari-AAK and Kronecker theorems, and provides conditions for the existence of solutions of product Pick problems through finite Picktype matrices. We give geometric and duality characterizations of BMOr, and of a subspace of it, bmo, closely linked withA
2 weights. This completes some aspects of the theory of BMO in product spaces.Sadosky was partially supported by NSF grants DMS-9205926, INT-9204043 and GER-9550373, and her visit to MSRI is supported by NSF grant DMS-9022140 to MSRI. 相似文献
18.
The C
*-algebra
generated by the n poly-Bergman and m antipoly-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space
L
2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky
results on two-dimensional convolution operators with symbols admitting homogeneous discontinuities we reduce the study to
simpler C
*-algebras associated with points
and pairs
. Applying a symbol calculus for the abstract unital C
*-algebras generated by N orthogonal projections sum of which equals the unit and by M = n + m one-dimensional orthogonal projections and using relations for the Gauss hypergeometric function, we study local algebras
at points
being the discontinuity points of coefficients. A symbol calculus for the C
*-algebra
is constructed and a Fredholm criterion for the operators
is obtained. 相似文献
19.
Salah Mecheri 《Integral Equations and Operator Theory》2005,53(3):403-409
Let B(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Let A = (A1,A2,.., An) and B = (B1, B2,.., Bn) be n-tuples in B(H), we define the elementary operator
by
In this paper we initiate the study of some properties of the range of such operators. 相似文献
20.
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