scholarly journals Invariant subspaces for bounded operators with large localizable spectrum

2001 ◽  
Vol 129 (8) ◽  
pp. 2365-2372
Author(s):  
Bebe Prunaru
Keyword(s):  
Invariant Subspaces ◽  
Bounded Operators ◽  
Localizable Spectrum

scholarly journals Invariant subspaces for polynomially bounded operators

2004 ◽  
Vol 213 (2) ◽  
pp. 321-345 ◽  
Author(s):  
Călin Ambrozie ◽  
Vladimı́r Müller
Keyword(s):  
Invariant Subspaces ◽  
Bounded Operators ◽  
Polynomially Bounded Operators

Invariant subspaces and localizable spectrum

2002 ◽  
Vol 42 (4) ◽  
pp. 461-471 ◽  
Author(s):  
J�rg Eschmeier ◽  
Bebe Prunaru
Keyword(s):  
Invariant Subspaces ◽  
Localizable Spectrum

scholarly journals Operadores de riesz en el Alglat(T)∩{T}

2021 ◽  
Vol 6 (1) ◽  
pp. 49
Author(s):  
Edixo Rosales
Keyword(s):  
Banach Space ◽  
Invariant Subspaces ◽  
Bounded Operators ◽  
Riesz Operator ◽  
Palabras Clave ◽  
Bounded Below

  En este trabajo X es un espacio de Banach y B(X) denota los operadores acotados. Si T∈B(X), por lat(T) entenderemos los subespacios invariantes por T. Se dice que T es lleno, si (T(M)) ̅=M, para todo M∈lat(T) (la barra indica la clausura en la topología inducida por la norma). Se prueba principalmente el siguiente resultado: Sean X un espacio de Banach y T ∈B(X) acotado por abajo. Sea K ∈Alglat(T)∩{T}' un operador de Riesz. Si K es lleno, entonces T es lleno. Aquí Alglat(T)={S∈B(X):M∈lat(T)⟾M∈lat(S)} y {T}^'={S∈B(X):S∘T=T∘S}.   Palabras clave: Operador lleno, operador de Riesz, operador acotado por abajo.   Abstract In this work X is a Banach space and B(X) denotes the bounded operators. If T ∈B(X), for lat(T) we will understand the invariant subspaces for T. An operator T is full, if (T(M)) ̅=M, for all M∈ latT (the bar indicates the closure in the topology induced by the norm). The following result is true: Let X be a Banach space, T ∈B(X) a bounded below operator and K ∈Alglat(T)∩{T}' a Riesz operator: If K is a full operator, then T is a full operator. Here Alglat(T)={S∈B(X):M∈lat(T)⟾M∈lat(S)} and {T}^'={S∈B(X):S∘T=T∘S}.   Keywords: full operator, Riesz operator, bounded below operator.  

ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES

2019 ◽  
Vol 99 (2) ◽  
pp. 274-283
Author(s):  
AMANOLLAH ASSADI ◽  
MOHAMAD ALI FARZANEH ◽  
HAJI MOHAMMAD MOHAMMADINEJAD
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Closed Subspace ◽  
Invariant Subspaces ◽  
Weak Limit ◽  
Linear Operators ◽  
Sufficient Condition ◽  
Bounded Operators ◽  
Bounded Linear ◽  
Rank Operator

We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace as an almost-invariant subspace, can be decomposed into the sum of a multiple of the identity and a finite-rank operator.

Algebras Intertwining Normal and Decomposable Operators

1979 ◽  
Vol 31 (6) ◽  
pp. 1339-1344 ◽  
Author(s):  
Ali A. Jafarian
Keyword(s):  
Banach Space ◽  
Compact Operator ◽  
Invariant Subspaces ◽  
Complex Banach Space ◽  
Bounded Operators ◽  
Zero Eigenvalue ◽  
Infinite Dimensional ◽  
Decomposable Operators ◽  
Closed Invariant Subspace ◽  
Injective Operator

The celebrated result of Lomonosov [6] on the existence of invariant subspaces for operators commuting with a compact operator have been generalized in different directions (for example see [2], [7], [8], [9]). The main result of [9] (see also [7]) is: If is a norm closed algebra of (bounded) operators on an infinite dimensional (complex) Banach space , if K is a nonzero compact operator on , and if then has a non-trivial (closed) invariant subspace. In [7], it is mentioned that the above result holds if instead of compactness for K we assume that K is a non-invertible injective operator with a non-zero eigenvalue belonging to the class of decomposable, hyponormal, or subspectral operators.

Completely Reducible Operator Algebras and Spectral Synthesis

1982 ◽  
Vol 34 (5) ◽  
pp. 1025-1035 ◽  
Author(s):  
Shlomo Rosenoer
Keyword(s):  
Operator Algebras ◽  
Spectral Synthesis ◽  
Invariant Subspaces ◽  
Bounded Operators ◽  
Von Neumann ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Completely Reducible ◽  
Weakly Closed ◽  
Reductive Algebra

An algebra of bounded operators on a Hilbert space H is said to be reductive if it is unital, weakly closed and has the property that if M ⊂ H is a (closed) subspace invariant for every operator in , then so is M⊥. Loginov and Šul'man [6] and Rosenthal [9] proved that if is an abelian reductive algebra which commutes with a compact operator K having a dense range, then is a von Neumann algebra. Note that in this case every invariant subspace of is spanned by one-dimensional invariant subspaces. Indeed, the operator KK* commutes with . Hence its eigenspaces are invariant for , so that H is an orthogonal sum of the finite-dimensional invariant subspaces of From this our claim easily follows.

Invariant Subspaces on KPC-Hypergroups

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