scholarly journals Commutativity up to a factor of bounded operators in complex Hilbert space

2002 ◽  
Vol 458 (2017) ◽  
pp. 109-118 ◽  
Author(s):  
James A. Brooke ◽  
Paul Busch ◽  
David B. Pearson
Keyword(s):  
Hilbert Space ◽  
Complex Hilbert Space ◽  
Bounded Operators

scholarly journals Generators of reflexive algebras

1975 ◽  
Vol 20 (2) ◽  
pp. 159-164
Author(s):  
W. E. Longstaff
Keyword(s):  
Hilbert Space ◽  
Von Neumann Algebra ◽  
Complex Hilbert Space ◽  
Bounded Operators ◽  
Finitely Generated ◽  
Separable Space ◽  
Von Neumann ◽  
Underlying Space ◽  
Weakly Closed ◽  
Reflexive Algebras

For any collection of closed subspaces of a complex Hilbert space the set of bounded operators that leave invariant all the members of the collection is a weakly-closed algebra. The class of such algebras is precisely the class of reflexive algebras as defined for example in Radjavi and Rosenthal (1969) and contains the class of von Neumann algebras.In this paper we consider the problem of when such algebras are finitely generated as weakly-closed algebras. It is to be hoped that analysis of this problem may shed some light on the famous unsolved problem of whether every von Neumann algebra on a separable Hilbert space is finitely generated. The case where the underlying space is separable and the collection of subspaces is totally ordered is dealt with in Longstaff (1974). In the present paper the result of Longstaff (1974) is generalized to the case of a direct product of countably many totally ordered collections each on a separable space. Also a method of obtaining non-finitely generated reflexive algebras is given.

scholarly journals Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-6
Author(s):  
Dangui Yan ◽  
Chengchang Zhang
Keyword(s):  
Hilbert Space ◽  
Closed Subspace ◽  
Complex Hilbert Space ◽  
Generalized Derivations ◽  
Nest Algebra ◽  
Bounded Operators ◽  
Subspace Lattice ◽  
Nest Algebras

LetHbe a complex Hilbert space andB(H)the collection of all linear bounded operators,Ais the closed subspace lattice including 0 anH, thenAis a nest, accordingly algA={T∈B(H):TN⊆N,  ∀N∈A}is a nest algebra. It will be shown that of nest algebra, generalized derivations are generalized inner derivations, and bilocal Jordan derivations are inner derivations.

REPRESENTATIONS OF LIE ALGEBRAS BUILT OVER HILBERT SPACE

2011 ◽  
Vol 14 (03) ◽  
pp. 419-442
Author(s):  
PALLE E. T. JORGENSEN
Keyword(s):  
Hilbert Space ◽  
Lie Algebras ◽  
Fock Space ◽  
Quantum Statistical Mechanics ◽  
Complex Hilbert Space ◽  
Tensor Algebra ◽  
Bounded Operators ◽  
Inductive Limits ◽  
Tensor Algebras ◽  
Representations Of Lie Algebras

Starting with a complex Hilbert space, using inductive limits, we build Lie algebras, and find families of representations. They include those often studied in mathematical physics in order to model quantum statistical mechanics or quantum fields. We explore natural actions on infinite tensor algebras T(H) built with a functorial construction, starting with a fixed Hilbert space H. While our construction applies also when H is infinite-dimensional, the case with N ≔ dim H finite is of special interest as the symmetry group we consider is then a copy of the non-compact Lie group U(N, 1). We give the tensor algebra T(H) the structure of a Hilbert space, i.e. the unrestricted infinite tensor product Fock space [Formula: see text]. The tensor algebra T(H) is naturally represented as acting by bounded operators on [Formula: see text], and U (N, 1) as acting as a unitary representation. From this we built a covariant system, and we explore how the fermion, the boson, and the q on Hilbert spaces are reduced by the representations. In particular we display the decomposition into irreducible representations of the naturally defined U (N, 1) representation.

scholarly journals Centers of mass for operator-families

1992 ◽  
Vol 34 (1) ◽  
pp. 123-126
Author(s):  
Makoto Takaguchi
Keyword(s):  
Hilbert Space ◽  
Numerical Range ◽  
Complex Hilbert Space ◽  
Bounded Operators ◽  
Centers Of Mass ◽  
Image Position ◽  
Joint Numerical Range

Let Hbe a complex Hilbert space and let B(H) be the algebra of (bounded) operators on H. Let A =(A,…,An) be an n-tuple of operators on H. The joint numerical range of A is the subset W(A) of ℂn such that

scholarly journals TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY

2010 ◽  
Vol 88 (2) ◽  
pp. 205-230 ◽  
Author(s):  
CHRISTOPH KRIEGLER ◽  
CHRISTIAN LE MERDY
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Unconditional Basis ◽  
Compact Set ◽  
Bounded Operators ◽  
Space Setting ◽  
Uniformly Bounded

AbstractLet K be any compact set. The C*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these results to the Banach space setting, using the key concept ofR-boundedness. Then we apply these results to operators with a uniformly bounded H∞-calculus, as well as to unconditionality on Lp. We show that any unconditional basis on Lp ‘is’ an unconditional basis on L2 after an appropriate change of density.

scholarly journals Traces of localisation operators with two admissible wavelets

2003 ◽  
Vol 45 (1) ◽  
pp. 17-25 ◽  
Author(s):  
M. W. Wong ◽  
Zhaohui Zhang
Keyword(s):  
Hilbert Space ◽  
Complex Hilbert Space ◽  
Resolution Of The Identity

AbstractThe resolution of the identity formula for a localisation operator with two admissible wavelets on a separable and complex Hilbert space is given and the traces of these operators are computed.

scholarly journals Some inequalities for trace class operators via a Kato’s result

2017 ◽  
Vol 11 (01) ◽  
pp. 1850004
Author(s):  
S. S. Dragomir
Keyword(s):  
Hilbert Space ◽  
Power Series ◽  
Trace Class ◽  
Complex Hilbert Space ◽  
Normal Operators ◽  
Trace Class Operators ◽  
Kato’S Inequality ◽  
New Inequalities

By the use of the celebrated Kato’s inequality, we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space [Formula: see text] Natural applications for functions defined by power series of normal operators are given as well.

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