The orthogonal projections with respect to a periodic continuous unitary representation of the group (R,+) on a complex Hilbert space

2014 ◽  
Author(s):  
Seda Öztürk
Keyword(s):  
Hilbert Space ◽  
Unitary Representation ◽  
Complex Hilbert Space ◽  
Orthogonal Projections ◽  
Continuous Unitary Representation

On Permutability and Submultiplicativity of Spectral Radius

1995 ◽  
Vol 47 (5) ◽  
pp. 1007-1022 ◽  
Author(s):  
W. E. Longstaff ◽  
H. Radjavi
Keyword(s):  
Hilbert Space ◽  
Spectral Radius ◽  
Compact Operators ◽  
Complex Hilbert Space ◽  
Semigroup Of Operators ◽  
Multiplicative Semigroup ◽  
Orthogonal Projections ◽  
Normal Operators

AbstractLet r(T) denote the spectral radius of the operator T acting on a complex Hilbert space H. Let S be a multiplicative semigroup of operators on H. We say that r is permutable on 𝓢 if r(ABC) = r(BAC), for every A,B,C ∈ 𝓢. We say that r is submultiplicative on 𝓢 if r(AB) ≤ r(A)r(B), for every A, B ∈ 𝓢. It is known that, if r is permutable on 𝓢, then it is submultiplicative. We show that the converse holds in each of the following cases: (i) 𝓢 consists of compact operators (ii) 𝓢 consists of normal operators (iii) 𝓢 is generated by orthogonal projections.

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.

Nonlinear ∗-Jordan triple derivations on von Neumann algebras

2018 ◽  
Vol 68 (1) ◽  
pp. 163-170 ◽  
Author(s):  
Fangfang Zhao ◽  
Changjing Li
Keyword(s):  
Hilbert Space ◽  
Von Neumann Algebra ◽  
Von Neumann Algebras ◽  
New Product ◽  
Complex Hilbert Space ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Von Neumann

AbstractLetB(H) be the algebra of all bounded linear operators on a complex Hilbert spaceHand 𝓐 ⊆B(H) be a von Neumann algebra with no central summands of typeI1. ForA,B∈ 𝓐, define byA∙B=AB+BA∗a new product ofAandB. In this article, it is proved that a map Φ: 𝓐 →B(H) satisfies Φ(A∙B∙C) = Φ(A) ∙B∙C+A∙ Φ(B) ∙C+A∙B∙Φ(C) for allA,B,C∈ 𝓐 if and only if Φ is an additive *-derivation.

Representation of Symmetries and Observables in Functional Hilbert Space. II.

1972 ◽  
Vol 27 (1) ◽  
pp. 7-22 ◽  
Author(s):  
A. Rieckers
Keyword(s):  
Hilbert Space ◽  
Relativistic Quantum ◽  
Preceding Paper ◽  
Complex Hilbert Space ◽  
Unbounded Operators ◽  
Test Function ◽  
Test Function Space ◽  
Quantum Observables ◽  
Set Up ◽  
Real Test

Abstract The representation of infinitesimal generators corresponding to the group representation dis-cussed in the preceding paper is analyzed in the Hilbert space of functionals over real test functions. Explicit expressions for these unbounded operators are constructed by means of the functio-nal derivative and by canonical operator pairs on dense domains. The behaviour under certain basis transformations is investigated, also for non-Hermitian generators. For the Hermitian ones a common, dense domain is set up where they are essentially selfadjoint. After having established a one-to-one correspondence between the real test function space and a complex Hilbert space the theory of quantum observables is applied to the functional version of a relativistic quantum field theory.

On Operator Algebras and Invariant Subspaces

1969 ◽  
Vol 21 ◽  
pp. 1178-1181 ◽  
Author(s):  
Chandler Davis ◽  
Heydar Radjavi ◽  
Peter Rosenthal
Keyword(s):  
Hilbert Space ◽  
Elementary Proof ◽  
Operator Algebras ◽  
Equivalent Form ◽  
Invariant Subspaces ◽  
Complex Hilbert Space ◽  
Closed Algebra ◽  
Weakly Closed ◽  
Special Case

If is a collection of operators on the complex Hilbert space , then the lattice of all subspaces of which are invariant under every operator in is denoted by Lat . An algebra of operators on is defined (3; 4) to be reflexive if for every operator B on the inclusion Lat ⊆ Lat B implies .Arveson (1) has proved the following theorem. (The abbreviation “m.a.s.a.” stands for “maximal abelian self-adjoint algebra”.)ARVESON's THEOREM. Ifis a weakly closed algebra which contains an m.a.s.a.y and if Lat, then is the algebra of all operators on .A generalization of Arveson's Theorem was given in (3). Another generalization is Theorem 2 below, an equivalent form of which is Corollary 3. This theorem was motivated by the following very elementary proof of a special case of Arveson's Theorem.

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