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© Hindawi Publishing Corp. DUALITY OF MEASURE AND CATEGORY IN INFINITEDIMENSIONAL SEPARABLE HILBERT SPACE 2
, 2001
"... We prove that an analogy of the Oxtoby duality principle is not valid for the concrete ..."
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We prove that an analogy of the Oxtoby duality principle is not valid for the concrete
Broken tubes in Hilbert spaces
 Analysis
"... Abstract. A broken tube is a special kind of a domain in an infinitedimensional separable Hilbert space, and it has several properties which do not occur in a finitedimensional space. 1 ..."
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Abstract. A broken tube is a special kind of a domain in an infinitedimensional separable Hilbert space, and it has several properties which do not occur in a finitedimensional space. 1
Local automorphisms of the unitary group and the general linear group on a Hilbert space
 MR 1763889 (2001a:47083), Zbl 0963.46044
"... We prove that every 2local automorphism of the unitary group or the general linear group on a complex infinitedimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their local actions on the twopoints subsets of the groups in ques ..."
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Cited by 4 (0 self)
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We prove that every 2local automorphism of the unitary group or the general linear group on a complex infinitedimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their local actions on the twopoints subsets of the groups
TIGHT PROJECTIONS OF FRAMES ON INFINITE DIMENSIONAL HILBERT SPACES
"... Abstract. We characterize the frames on an infinite dimensional separable Hilbert space that can be projected to a tight frame for an infinite dimensional subspace. A result of Casazza and Leon states that an arbitrary frame for a 2N – or (2N −1)–dimensional Hilbert space can be projected to a tight ..."
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Abstract. We characterize the frames on an infinite dimensional separable Hilbert space that can be projected to a tight frame for an infinite dimensional subspace. A result of Casazza and Leon states that an arbitrary frame for a 2N – or (2N −1)–dimensional Hilbert space can be projected to a
SINGULAR COMMUTING PERTURBATIONS OF OPERATORS AND HYPONORMALITY
"... an infinitedimensional, separable Hilbert space. Suppose that A is absolutely continuous and that D is purely singular, in which case it is shown that A + D is also absolutely continuous. Corresponding to an absolutely continuous selfadjoint operator is a certain series each term of which is the me ..."
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an infinitedimensional, separable Hilbert space. Suppose that A is absolutely continuous and that D is purely singular, in which case it is shown that A + D is also absolutely continuous. Corresponding to an absolutely continuous selfadjoint operator is a certain series each term of which
Sums and products of weighted shifts
 Canad. Math. Bull
, 2001
"... Abstract. In this article it is shown that every bounded linear operator on a complex, infinite dimensional, separable Hilbert space is a sum of at most eighteen unilateral (alternatively, bilateral) weighted shifts. As well, we classify products of weighted shifts, as well as sums and limits of the ..."
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Abstract. In this article it is shown that every bounded linear operator on a complex, infinite dimensional, separable Hilbert space is a sum of at most eighteen unilateral (alternatively, bilateral) weighted shifts. As well, we classify products of weighted shifts, as well as sums and limits
ON THE SPECTRUM OF INFINITE DIMENSIONAL RANDOM PRODUCTS OF COMPACT OPERATORS
, 709
"... Abstract. We consider an infinite dimensional separable Hilbert space and its family of compact integrable cocycles over a dynamical system f. Assuming that f acts in a compact Hausdorff space X and preserves a Borel regular ergodic measure which is positive on nonempty open sets, we conclude that ..."
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Abstract. We consider an infinite dimensional separable Hilbert space and its family of compact integrable cocycles over a dynamical system f. Assuming that f acts in a compact Hausdorff space X and preserves a Borel regular ergodic measure which is positive on nonempty open sets, we conclude
An infinite dimensional version of the Schur convexity property and applications
, 2007
"... We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators that can be approximated by operato ..."
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We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of linear selfadjoint operators that can be approximated
Min and MaxEntropies as Generalized Entropy Measures in InfiniteDimensional Quantum Systems
, 2009
"... Since the introduction of the (smooth) min and maxentropy, various results have affirmed their fundamental importance in quantum information theory. In this thesis we investigate the behavior of these entropies for quantum systems with infinitedimensional separable Hilbert spaces. As a main resul ..."
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Since the introduction of the (smooth) min and maxentropy, various results have affirmed their fundamental importance in quantum information theory. In this thesis we investigate the behavior of these entropies for quantum systems with infinitedimensional separable Hilbert spaces. As a main
ON THE MEASURABILITY OF ADDITIVE FUNCTIONALS
"... Abstract. For an infinitedimensional separable Hilbert space H, the problem of measurability of additive functionals f: H → R with respect to various extensions of σfinite diffused Borel measures on H is discussed. It is shown that there exists an everywhere discontinuous additive functional f on ..."
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Abstract. For an infinitedimensional separable Hilbert space H, the problem of measurability of additive functionals f: H → R with respect to various extensions of σfinite diffused Borel measures on H is discussed. It is shown that there exists an everywhere discontinuous additive functional f
Results 1  10
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1,816