Note on invariant subspaces of a compact normal operator

1963 ◽  
Vol 14 (1) ◽  
pp. 337-340 ◽  
Author(s):  
Tsuyoshi And�
Keyword(s):  
Normal Operator ◽  
Invariant Subspaces ◽  
Compact Normal Operator

scholarly journals The boundary of the numerical range

1981 ◽  
Vol 22 (1) ◽  
pp. 69-72 ◽  
Author(s):  
G. de Barra
Keyword(s):  
Hilbert Space ◽  
Convex Hull ◽  
Similar Condition ◽  
Point Spectrum ◽  
Numerical Range ◽  
Normal Operator ◽  
Density Condition ◽  
Compact Normal Operator

In [1] it was shown that for a compact normal operator on a Hilbert space the numerical range was the convex hull of the point spectrum. Here it is shown that the same holds for a semi-normal operator whose point spectrum satisfies a density condition (Theorem 1). In Theorem 2 a similar condition is shown to imply that the numerical range of a semi-normal operator is closed. Some examples are given to indicate that the condition in Theorem 1 cannot be relaxed too much.

scholarly journals Non-negative Integer Power of a Hyponormal m-isometry is Reflexive

2021 ◽  
pp. 1-5
Author(s):  
Pradeep Kothiyal ◽  
Rajesh Kumar Pal ◽  
Deependra Nigam
Keyword(s):  
Dimensional Space ◽  
Normal Operator ◽  
Invariant Subspaces ◽  
Negative Integer ◽  
Finite Dimensional Space ◽  
Integer Power ◽  
Finite Dimensional ◽  
Normal Operators ◽  
Reflexive Operator

Sarason did pioneer work on reflexive operator and reflexivity of normal operators, however, he did not used the word reflexive but his results are equivalent to say that every normal operator is reflexive. The word reflexive was suggested by HALMOS and first appeared in H. Rajdavi and P. Rosenthals book `Invariant Subspaces’ in 1973. This line of research was continued by Deddens who showed that every isometry in B(H) is reflexive. R. Wogen has proved that `every quasi-normal operator is reflexive’. These results of Deddens, Sarason, Wogen are particular cases of theorem of Olin and Thomson which says that all sub-normal operators are reflexive. In other direction, Deddens and Fillmore characterized these operators acting on a finite dimensional space are reflexive. J. B. Conway and Dudziak generalized the result of reflexivity of normal, quasi-normal, sub-normal operators by proving the reflexivity of Vonneumann operators. In this paper we shall discuss the condition under which m-isometries operators turned to be reflexive.

scholarly journals On the eigenvalues which express antieigenvalues

2005 ◽  
Vol 2005 (10) ◽  
pp. 1543-1554 ◽  
Author(s):  
Morteza Seddighin ◽  
Karl Gustafson
Keyword(s):  
Normal Operator ◽  
Compact Normal Operator

We showed previously that the first antieigenvalue and the components of the first antieigenvectors of an accretive compact normal operator can be expressed either by a pair of eigenvalues or by a single eigenvalue of the operator. In this paper, we pin down the eigenvalues ofTthat express the first antieigenvalue and the components of the first antieigenvectors. In addition, we will prove that the expressions which state the first antieigenvalue and the components of the first antieigenvectors are unambiguous. Finally, based on these new results, we will develop an algorithm for computing higher antieigenvalues.

scholarly journals Invariant subspaces of a normal operator

1959 ◽  
Vol 26 (1) ◽  
pp. 95-111 ◽  
Author(s):  
James E. Scroggs
Keyword(s):  
Normal Operator ◽  
Invariant Subspaces

Finite Rank Operators and Functional Calculus on Hilbert Modules over Abelian C*-Algebras

1997 ◽  
Vol 40 (2) ◽  
pp. 193-197 ◽  
Author(s):  
Dan Kucerovsky
Keyword(s):  
Finite Rank ◽  
Functional Calculus ◽  
Normal Operator ◽  
Hilbert Module ◽  
Hilbert Modules ◽  
Finitely Generated ◽  
C Algebras ◽  
Finite Rank Operators ◽  
Compact Normal Operator

AbstractWe consider the problem: If K is a compact normal operator on a Hilbert module E, and f ∈ C0(SpK) is a function which is zero in a neighbourhood of the origin, is f(K) of finite rank? We show that this is the case if the underlying C*-algebra is abelian, and that the range of f(K) is contained in a finitely generated projective submodule of E.

Invariant Subspaces on KPC-Hypergroups

2019 ◽  
Vol 15 (1) ◽  
pp. 122-130
Author(s):  
Laszlo Szekelyhidi ◽  
◽  
Seyyed Mohammad Tabatabaie ◽  
Keyword(s):  
Invariant Subspaces

Invariant Subspaces

1973 ◽  
Author(s):  
Heydar Radjavi ◽  
Peter Rosenthal
Keyword(s):  
Invariant Subspaces
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