共查询到20条相似文献,搜索用时 62 毫秒
1.
Israel Gohberg Seymour Goldberg Naum Krupnik 《Integral Equations and Operator Theory》2001,40(4):441-453
SupposeA is a bounded linear operator on a separable Hilbert space withA
m
of trace class for some positive integerm. A generalized determinant for the operatorI–A is defined, its properties studied and this determinant is then used to exhibit an inversion formula forI–A. 相似文献
2.
It is shown that the classical Volterra operator, which is cyclic, is not supercyclic on any of the spaces Lp[0, 1], 1 p < . This solves a question posed by Héctor Salas. This contrasts with the fact that the derivative operator, the left inverse of the Volterra operator, although unbounded, is hypercyclic on Lp[0, 1]. 相似文献
3.
Alexander Kovačec 《Order》1989,6(3):245-263
Consider two partially ordered setsP, Q and a number of edges connecting some of the points ofP with some of the points ofQ. This yields a bipartite graph. Some pairs of the edges may cross each other because their endpoints atP andQ are oppositely ordered. A natural decrossing operation is to exchange the endpoints of these edges incident atQ, say. This is called a switch. A left lift of an edge means to replace its starting point atP by a larger starting point. A right lift is defined symmetrically for the endpoints atQ. The operation of adding an edge cannot, informally, be explained better. Assume we are given two bipartite graphs , on the node setPQ. We show that for certain pairs (P, Q) of finite posets, a neat necessary and sufficient criterion can be given in order that is obtainable from by the sequence of elementary operations just defined. A recent characterization of the Bruhat order of the symmetric group follows as a special case. 相似文献
4.
Stephan Ramon Garcia 《Integral Equations and Operator Theory》2008,60(3):357-367
If denotes the polar decomposition of a bounded linear operator T, then the Aluthge transform of T is defined to be the operator . In this note we study the relationship between the Aluthge transform and the class of complex symmetric operators (T iscomplex symmetric if there exists a conjugate-linear, isometric involution so that T = CT*C). In this note we prove that: (1) the Aluthge transform of a complex symmetric operator is complex symmetric, (2) if T is complex symmetric, then and are unitarily equivalent, (3) if T is complex symmetric, then if and only if T is normal, (4) if and only if T
2 = 0, and (5) every operator which satisfies T
2 = 0 is necessarily complex symmetric.
This work partially supported by National Science Foundation Grant DMS 0638789. 相似文献
5.
Dariusz Zagrodny 《Set-Valued Analysis》1996,4(4):301-314
In the paper we deal with the problem when the graph of the subdifferential operator of a convex lower semicontinuous function has a common point with the product of two convex nonempty weak and weak* compact sets, i.e. when graph (Q × Q
*) 0. The results obtained partially solve the problem posed by Simons as well as generalize the Rockafellar Maximal Monotonicity Theorem. 相似文献
6.
Robert Carroll 《Acta Appl Math》1986,6(2):109-184
This article represents a survey of transmutation ideas and their interaction with typical physical problems. For linear second-order differential operatorsP andQ one deals with canonical connectionsB:PQ (transmutations) satisfyingQB=BP and the related transport of structure between the theories ofP andQ. One can study in an intrinsic manner, e.g., Parseval formulas, eigenfunction expansions, integral transform, special functions, inverse problems, integral equations, and related stochastic filtering and estimation problems, etc. There are applications in virtually any area where such operators arise. 相似文献
7.
J. J. Koliha 《Aequationes Mathematicae》1977,16(1-2):31-35
The paper gives a necessary and sufficient condition on the spectrum of a bounded linear operator on Banach space for the convergence of the series
0
T(I-T
2)
n
. Some properties of the sum are investigated. 相似文献
8.
LetH be a Hilbert space andRHH be a bounded linear operator represented by an operator matrix which is a sum of a diagonal and of a semiseparable type of order one operator matrices. We consider three methods for solution of the operator equationRx=y. The obtained results yields new algorithms for solution of integral equations and for inversion of matrices. 相似文献
9.
Ruey-Jen Jang-Lewis Harold Dean Victory Jr. 《Integral Equations and Operator Theory》1994,18(1):88-108
LetE be a Banach lattice having order continuous norm. Suppose, moreover,T is a nonnegative reducible operator having a compact iterate and which mapsE into itself. The purpose of this work is to extend the previous results of the authors, concerning nonnegative solvability of (kernel) operator equations on generalL
p-spaces. In particular, we provide necessary and sufficient conditions for the operator equation x=T
x+y to possess a nonnegative solutionxE wherey is a given nonnegative and nontrivial element ofE and is any given positive parameter. 相似文献
10.
Yu. M. Arlinskii S. Hassi H. S. V. de Snoo 《Integral Equations and Operator Theory》2005,53(2):153-189
In this paper operator-valued Q-functions of Krein-Ovcharenko type are introduced. Such functions arise from the extension theory of Hermitian contractive
operators A in a Hilbert space ℌ. The definition is related to the investigations of M.G. Krein and I.E. Ovcharenko of the so-called
Qμ- and QM-functions. It turns out that their characterizations of such functions hold true only in the matrix valued case. The present
paper extends the corresponding properties for wider classes of selfadjoint contractive extensions of A. For this purpose some peculiar but fundamental properties on the behaviour of operator ranges of positive operators will
be used. Also proper characterizations for Qμ- and QM-functions in the general operator-valued case are given. Shorted operators and parallel sums of positive operators will be
needed to give a geometric understanding of the function-theoretic properties of the corresponding Q-functions. 相似文献
11.
For a contraction operator T with spectral radius less than one on a Banach space
, it is shown that the factorization of certain L1 functions by vectors x in
and x*. in
, in the sense that
for n ≧ 0, implies the existence of invariant subspaces for T. Explicit formulae for such factorizations are given in the case of weighted composition operators on reproducing kernel
Hilbert spaces. An interpolation result of McPhail is applied to show how this can be used to construct invariant subspaces
of hyperbolic weighted composition operators on H2.
Received: 1 November 2005 相似文献
12.
Vladimír Müller 《Integral Equations and Operator Theory》2001,41(2):230-253
LetT be an operator on a Banach spaceX. We give a survey of results concerning orbits {T
n
x:n=0,1,...} and weak orbits {T
n
x,x
*:n=0,1,...} ofT wherexX andx
*X
*. Further we study the local capacity of operators and prove that there is a residual set of pointsxX with the property that the local capacity cap(T, x) is equal to the global capacity capT. This is an analogy to the corresponding result for the local spectral radius.The research was supported by the grant No. A1019801 of AV R. 相似文献
13.
Gilles Pisier 《Integral Equations and Operator Theory》1998,31(3):353-370
There is a pair of commuting operators (T
1,T
2) on Hilbert space such that eachT
1 andT
2 is similar to a contraction but the pair (T
1,T
2) is not similar to a pair of contractions. There is a pair of commuting unitarizable representations (1,2) on the free group withN2 generators such that (1,2) is not similar to a pair of unitary representations. In connection with these examples, we introduce and study a notion of length for aC
*-algebra (or an operator algebra) generated by two subalgebras, which is analogous to the minimum length of a word in the generators of a group.Partially supported by the N.S.F. 相似文献
14.
Families of pairs of matrix-valued meromorphic functions
(,P) depending on two parameters andP are introduced. They are the projective analogues of classes of functions studied in [1] and include as special cases the projective Schur, Nevanlinna and Carathéodory classes. A two sided Nevanlinna-Pick interpolation problem is defined and solved in
(,P), using the fundamental matrix inequality method. 相似文献
15.
Let the functionQ be holomorphic in he upper half plane + and such that ImQ(z 0 and ImzQ(z) 0 ifz +. A basic result of M.G. Krein states that these functionsQ are the principal Titchmarsh-Weyl coefficiens of a (regular or singular) stringS[L,m] with a (non-decreasing) mass distribution functionm on some interval [0,L) with a free left endpoint 0. This string corresponds to the eigenvalue problemdf +
fdm = 0; f(0–) = 0. In this note we show that the set of functionsQ which are holomorphic in + and such that the kernel
has negative squares of + and ImzQ(z) 0 ifz + is the principal Titchmarsh-Weyl coefficient of a generalized string, which is described by the eigenvalue problemdf +f
dm +
2
fdD = 0 on [0,L),f(0–) = 0. Here is the number of pointsx whereD increases or 0 >m(x + 0) –m(x – 0) –; outside of these pointsx the functionm is locally non-decreasing and the functionD is constant.To the memory of M.G. Krein with deep gratitude and affection.This author is supported by the Fonds zur Förderung der wissenschaftlichen Forschung of Austria, Project P 09832 相似文献
16.
For a finite ordered set P, let c(P) denote the cardinality of the largest subset Q such that the induced suborder on Q satisfies the Jordan-Dedekind chain condition (JDCC), i.e., every maximal chain in Q has the same cardinality. For positive integers n, let f(n) be the minimum of c(P) over all ordered sets P of cardinality n. We prove:
相似文献
17.
Let {n}
n=0
be the eigenvalue sequence of a symmetric Hilbert-Schmidt operator onL
2(I). WhenI is an open interval, a necessary condition for {n}
n=0
to be in the sequence space is obtained. WhenI is a closed bounded interval, sufficient conditions for {n}
n=0
to be in the sequence space – are obtained. 相似文献
18.
19.
LetH be a complex infinite-dimensional separable Hilbert space. An operatorT inL(H) is called totally P-posinormal (see [9]) iff there is a polynomialP with zero constant term such that
for each
, whereT
z
=T–zI andM(z) is bounded on the compacts of C. In this paper we prove that every totally P-posinormal operator is subscalar, i.e. it is the restriction of a generalized scalar operator to an invariant subspace. Further, a list of some important corollaries about Bishop's property and the existence of invariant subspaces is presented. 相似文献
20.
Let H be a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator A in L(H) is said to be a Cowen-Douglas operator if there exist Ω, a connected open subset of complex plane C, and n, a positive integer, such that
- (a)
- (b)
- for z in Ω;
- (c)
- ; and
- (d)
- for z in Ω.