scholarly journals Stable invariant subspaces for operators on Hilbert space

1997 ◽  
Vol 66 ◽  
pp. 49-61 ◽  
Author(s):  
John Conway ◽  
Don Hadwin
Keyword(s):  
Hilbert Space ◽  
Invariant Subspaces ◽  
Stable Invariant

scholarly journals Biquasitriangularity and spectral continuity

1985 ◽  
Vol 26 (2) ◽  
pp. 177-180 ◽  
Author(s):  
Ridgley Lange
Keyword(s):  
Hilbert Space ◽  
Sufficient Conditions ◽  
Invariant Subspaces ◽  
Extension Property ◽  
Point Of View ◽  
Single Valued Extension Property ◽  
Continuity Theorem ◽  
Spectral Continuity ◽  
Necessary And Sufficient ◽  
Continuity Of The Spectrum

In [6] Conway and Morrell characterized those operators on Hilbert space that are points of continuity of the spectrum. They also gave necessary and sufficient conditions that a biquasitriangular operator be a point of spectral continuity. Our point of view in this note is slightly different. Given a point T of spectral continuity, we ask what can then be inferred. Several of our results deal with invariant subspaces. We also give some conditions characterizing a biquasitriangular point of spectral continuity (Theorem 3). One of these is that the operator and its adjoint both have the single-valued extension property.

On Regular Generalized Sampling in T-Invariant Subspaces of a Hilbert Space: An Overview

2019 ◽  
Vol 41 (6) ◽  
pp. 685-709
Author(s):  
Antonio G. García ◽  
María J. Muñoz-Bouzo ◽  
Gerardo Pérez-Villalón
Keyword(s):  
Hilbert Space ◽  
Invariant Subspaces ◽  
Generalized Sampling

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.

On Reflexivity of Algebras

1981 ◽  
Vol 33 (6) ◽  
pp. 1291-1308 ◽  
Author(s):  
Mehdi Radjabalipour
Keyword(s):  
Hilbert Space ◽  
Natural Number ◽  
Separable Hilbert Space ◽  
Invariant Subspaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Closed Algebra ◽  
Direct Sum ◽  
Weakly Closed

For each natural number n we define to be the class of all weakly closed algebras of (bounded linear) operators on a separable Hilbert space H such that the lattice of invariant subspaces of and (alg lat )(n) are the same. (If A is an operator, A(n) denotes the direct sum of n copies of A; if is a collection of operators,. Also, alg lat denotes the algebra of all operators leaving all invariant subspaces of invariant.) In the first section we show that . In Section 2 we prove that every weakly closed algebra containing a maximal abelian self adjoint algebra (m.a.s.a.) is , and that . It is also shown that certain algebras containing a m.a.s.a. are necessarily reflexive.

Compact Operators in Reductive Algebras

1975 ◽  
Vol 27 (1) ◽  
pp. 152-154
Author(s):  
Edward A. Azoff
Keyword(s):  
Hilbert Space ◽  
Invariant Subspaces ◽  
Compact Operators ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Term Algebra

Let be a Hilbert space and denote the collection of (bounded, linear) operators on by . Throughout this paper, the term ‘algebra’ will refer to a subalgebra of ; unless otherwise stated, it will not be assumed to contain I or to be closed in any topology.An algebra is said to be transitive if it has no non-trivial invariant subspaces. The following lemma has revolutionized the study of transitive algebras. For a pr∞f and a general discussion of its implications, the reader is referred to [5].

scholarly journals Stable and norm-stable invariant subspaces

2013 ◽  
Vol 69 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Alexander Borichev ◽  
Don Hadwin ◽  
Hassan Yousefi
Keyword(s):  
Invariant Subspaces ◽  
Stable Invariant
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