Invariant Subspaces for Some Compact Perturbations of Normal Operators

2010 ◽  
pp. 14-18
Author(s):  
Mingxue Liu
Keyword(s):  
Invariant Subspaces ◽  
Compact Perturbations ◽  
Normal Operators

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.

Compact perturbations of normal operators in a Krein space

1990 ◽  
Vol 42 (10) ◽  
pp. 1155-1161 ◽  
Author(s):  
T. Ya. Azizov ◽  
P. Ionas
Keyword(s):  
Krein Space ◽  
Compact Perturbations ◽  
Kreĭn Space ◽  
Normal Operators

Growth Conditions and Decomposable Operators

1974 ◽  
Vol 26 (6) ◽  
pp. 1372-1379 ◽  
Author(s):  
Mehdi Radjabalipour
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Sufficient Conditions ◽  
Invariant Subspaces ◽  
Growth Conditions ◽  
Bounded Linear ◽  
Normal Operators ◽  
Long Time ◽  
Decomposable Operators ◽  
The Subject

Throughout this paper T will denote a bounded linear operator which is defined on a Banach space and whose spectrum lies on a rectifiable Jordan curve J .The operators having some growth conditions on their resolvents have been the subject of discussion for a long time. Many sufficient conditions have been found to ensure that such operators have invariant subspaces [2 ; 3 ; 7 ; 8 ; 12 ; 13; 14; 21; 27; 28; 29], are S-operators [14], are quasidecomposable [9], are decomposable [4 ; 11], are spectral [7 ; 10 ; 15 ; 17], are similar to normal operators [16 ; 23 ; 25 ; 26], or are normal [15 ; 18 ; 22]. In this line we are going to show that many such operators are decomposable.

Compact Perturbations of Reflexive Algebras

1981 ◽  
Vol 33 (3) ◽  
pp. 685-700 ◽  
Author(s):  
Kenneth R. Davidson
Keyword(s):  
Unitary Operator ◽  
Operator Algebras ◽  
Invariant Subspaces ◽  
Compact Operators ◽  
Reverse Inclusion ◽  
Finite Dimensional ◽  
Compact Perturbations ◽  
Reflexive Algebras ◽  
The Ideal ◽  
Subspace Lattices

In this paper we study lattice properties of operator algebras which are invariant under compact perturbations. It is easy to see that if and are two operator algebras with contained in , then the reverse inclusion holds for their lattices of invariant subspaces. We will show that in certain cases, the assumption thats is contained in , where is the ideal of compact operators, implies that the lattice of is “approximately” contained in the lattice of . In particular, supposed and are reflexive and have commutative subspace lattices containing “enough” finite dimensional elements. We show (Corollary 2.8) that if is unitarily equivalent to a subalgebra of , then there is a unitary operator which carries all “sufficiently large” subspaces in lat into lat .

On Decomposability of Compact Perturbations of Normal Operators

1975 ◽  
Vol 27 (3) ◽  
pp. 725-735 ◽  
Author(s):  
M. Radjabalipour ◽  
H. Radjavi
Keyword(s):  
Hilbert Space ◽  
Characteristic Function ◽  
Imaginary Part ◽  
Contraction Operator ◽  
Cayley Transform ◽  
Space Operator ◽  
Schatten Class ◽  
Compact Perturbations ◽  
Normal Operators ◽  
Decomposable Operator

The main purpose of this paper is to show that a bounded Hilbert-space operator whose imaginary part is in the Schatten class Cp(1 ≦ p < ∞ ) is strongly decomposable. This answers affirmatively a question raised by Colojoara and Foias [6, Section 5(e), p. 218].In case 0 ≦ T* — T ∈ C1, it was shown by B. Sz.-Nagy and C. Foias [2, p. 442; 25, p. 337] that T has many properties analogous to those of a decomposable operator and by A. Jafarian [11] that T is strongly decomposable. The authors of [11] and [24] employ the properties of the characteristic function of the contraction operator obtained from the Cayley transform of T;

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