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1.
Tsuyoshi Ando 《Linear algebra and its applications》2009,431(12):2346-2358
Let (H,J) be a Krein space with selfadjoint involution J. Starting with a canonical representation of a J-selfadjoint projection, J-projection in short, as the sum of a J-positive projection and a J-negative one we study in detail the structure of a regular subspace, that is, the range of a J-projection. We treat the problem when the sum of two regular subspaces is again regular. We also treat the problem when the closure of the range of the product of a J-contraction and a J-expansion becomes regular. 相似文献
2.
Alejandra Maestripieri Francisco Martínez Pería 《Integral Equations and Operator Theory》2007,59(2):207-221
The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded)
J-selfadjoint operator A (with the unique factorization property) acting on a Krein space
and a suitable closed subspace
of
, the Schur complement
of A to
is defined. The basic properties of
are developed and different characterizations are given, most of them resembling those of the shorted of (bounded) positive
operators on a Hilbert space.
To the memory of Professor Mischa Cotlar 相似文献
3.
María Celeste Gonzalez 《Linear algebra and its applications》2011,434(1):370-378
In this work we extend Cordes inequality, McIntosh inequality and CPR-inequality for the operator seminorm defined by a positive semidefinite bounded linear operator A. 相似文献
4.
Let J=Ir⊕-In-r,0<r<n. An n×n complex matrix A is said to be J-Hermitian if JA=A∗J. An extension of the classical theory of Courant and Fischer on the Rayleigh ratio of Hermitian matrices is stated for J-Hermitian matrices. Applications to the theory of small oscilations of a mechanical system are presented. 相似文献
5.
《Mathematische Nachrichten》2018,291(5-6):879-896
A J‐frame for a Krein space is in particular a frame for (in the Hilbert space sense). But it is also compatible with the indefinite inner‐product of , meaning that it determines a pair of maximal uniformly definite subspaces, an analogue to the maximal dual pair associated with an orthonormal basis in a Krein space. This work is devoted to study duality for J‐frames in Krein spaces. Also, tight and Parseval J‐frames are defined and characterized. 相似文献
6.
7.
Agnes Meehyea Yang 《Integral Equations and Operator Theory》1994,19(4):477-499
A construction is made of a unitary linear system whose transfer function is a given power seriesB(z) with operator coefficients such that multiplication byB(z) is an everywhere defined transformation in the space of square summable power series with vector coefficients. A condition is also given for the existence of an observable linear system with such a transfer function. For both constructions properties of the spaces are given which imply essential uniqueness of linear systems with given transfer functions. A canonical conjugate-isometric linear system is uniquely determined by its transfer function whenever the state space is a Pontryagin space. 相似文献
8.
Assume that X, Y are real Banach spaces, Y has uniform convexity of type p (≥ 1), and f: X → Y is a standard coarse isometry. In this paper, we show that if
then there is a linear isometry U : X → Y so that
where is defined by
Representation properties of coarse isometries in free ultrafilter limits on are also discussed. 相似文献
9.
Mohammad Sal Moslehian 《Linear algebra and its applications》2011,434(8):1981-1987
We establish several operator versions of the classical Aczél inequality. One of operator versions deals with the weighted operator geometric mean and another is related to the positive sesquilinear forms. Some applications including the unital positive linear maps on C*-algebras and the unitarily invariant norms on matrices are presented. 相似文献
10.
In this paper we prove that a finite dimensional real normed linear space X is an inner product space iff for any linear operator T on X, T attains its norm at e1,e2∈SX implies T attains its norm at span{e1,e2}∩SX. 相似文献
11.
In this note we examine the relationships between p-hyponormal
operators and the operator inequality
. This leads to a method for
generating examples of p-hyponormal operators which are not q-hyponormal
for any
. Our methods are also shown to have implications for the class
of Furuta type inequalities. 相似文献
12.
Michał Wojtylak 《Integral Equations and Operator Theory》2007,59(1):129-147
The commutators of 2 × 2 block operator matrices with (unbounded) operator entries are investigated. The matrix representation
of a symmetric operator in a Krein space is exploited. As a consequence, the domination result due to Cichoń, Stochel and
Szafraniec is extended to the case of Krein spaces. 相似文献
13.
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
14.
M.S. Moslehian 《Linear algebra and its applications》2009,430(4):1131-1987
We give an extension of Hua’s inequality in pre-Hilbert C∗-modules without using convexity or the classical Hua’s inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert C∗-modules, another extension of Hua’s inequality is obtained. We also present an operator Hua’s inequality, which is equivalent to operator convexity of given continuous real function. 相似文献
15.
Fernanda Botelho 《Linear algebra and its applications》2010,432(1):275-282
We characterize essential normality for certain elementary operators acting on the Hilbert-Schmidt class. We find the Aluthge transform of an elementary operator of length one. We show that the Aluthge transform of an elementary 2-isometry need not be a 2-isometry. We also characterize hermitian elementary operators of length 2. 相似文献
16.
A Krein operator is a positive operator, acting on a partially ordered Banach space, that carries positive elements to strong units. The purpose of this paper is to present a survey of the remarkable spectral properties (most of which were established by M.G. Krein) of these operators. The proofs presented here seem to be simpler than the ones existing in the literature. Some new results are also obtained. For instance, it is shown that every positive operator on a Krein space which is not a multiple of the identity operator has a nontrivial hyperinvariant subspace.
Dedicated to the memory of M.G. Krein (1907–1989) 相似文献
17.
In this paper, we use the mosaic of a subnormal operator given by Daoxing Xia to give an alternate definition of the Pincus
principal function for pure subnormal operators. This allows us to provide much simplified proofs of some of the basic properties
of the principal function and of the Carey-Helton-Howe-Pincus Theorem in the subnormal case. 相似文献
18.
Let Cp be the Schatten p-class for p>0. Generalizations of the parallelogram law for the Schatten 2-norms have been given in the following form: if A={A1,A2,…,An} and B={B1,B2,…,Bn} are two sets of operators in, then C2
19.
It is shown that spaces of quasianalytic ultradifferentiable functions of Roumieu type ℰ{w}(Ω), on an open convex set , satisfy some new (Ω) -type linear topological invariants. Some consequences for the splitting of short exact sequences of
these spaces as well as for the structure of the spaces are derived. In particular, Fréchet quotients of ℰ{w}(Ω) have property (), while dual Fréchet quotients have property () of Vogt.
The work of P. Domański was supported by Committee of Scientific Research (KBN), Poland, grant P03A 022 25. 相似文献
20.
We study when a Banach space with absolute norm may have polynomial numerical indices equal to one. In the real case, we show that a Banach space X with absolute norm, which has the Radon-Nikodým property or is Asplund, satisfies n(2)(X)<1 unless it is one-dimensional. In the complex case, we show that the only Banach spaces X with absolute norm and the Radon-Nikodým property which satisfy n(2)(X)=1 are the spaces . Also, the only Asplund complex space X with absolute norm which satisfies n(2)(X)=1 is c0(Λ). 相似文献