A characterization of some subsets of S-essential spectra of a multivalued linear operator

2014 ◽  
Vol 135 (2) ◽  
pp. 171-186 ◽  
Author(s):  
Teresa Álvarez ◽  
Aymen Ammar ◽  
Aref Jeribi
Keyword(s):  
Linear Operator ◽  
Essential Spectra ◽  
Multivalued Linear Operator

scholarly journals Degenerate C-distribution cosine functions and degenerate C-ultradistribution cosine functions in locally convex spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3075-3089
Author(s):  
Daniel Velinov ◽  
Marko Kostic ◽  
Stevan Pilipovic
Keyword(s):  
Linear Operator ◽  
Infinitesimal Generator ◽  
Cosine Function ◽  
Locally Convex Spaces ◽  
Regularizing Operator ◽  
Multivalued Linear Operator ◽  
C Distribution ◽  
Locally Convex ◽  
Cosine Functions ◽  
Convex Spaces

The main purpose of this paper is to investigate degenerate C-(ultra)distribution cosine functions in the setting of barreled sequentially complete locally convex spaces. In our approach, the infinitesimal generator of a degenerate C-(ultra)distribution cosine function is a multivalued linear operator and the regularizing operator C is not necessarily injective. We provide a few important theoretical novelties, considering also exponential subclasses of degenerate C-(ultra)distribution cosine functions.

scholarly journals Antinormal composition operators on $ \mbf{\ell^2}$

2008 ◽  
Vol 39 (4) ◽  
pp. 347-352 ◽  
Author(s):  
Gyan Prakash Tripathi ◽  
Nand Lal
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Composition Operators ◽  
Complete Characterization ◽  
Inner Product ◽  
Complex Numbers ◽  
Bounded Linear ◽  
Normal Operators

A bounded linear operator $ T $ on a Hilbert space $ H $ is called antinormal if the distance of $ T $ from the set of all normal operators is equal to norm of $ T $. In this paper, we give a complete characterization of antinormal composition operators on $ \ell^2 $, where $ \ell^2 $ is the Hilbert space of all square summable sequences of complex numbers under standard inner product on it.

Stability of the S-essential spectra on a Banach space

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Faiçal Abdmouleh ◽  
Aymen Ammar ◽  
Aref Jeribi
Keyword(s):  
Banach Space ◽  
Linear Operators ◽  
Essential Spectra ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Riesz Projection

AbstractIn this paper, we give the characterization of S-essential spectra, we define the S-Riesz projection and we investigate the S-Browder resolvent. Finally, we study the S-essential spectra of sum of two bounded linear operators acting on a Banach space.

A separable quasidiagonal C*-algebra with a non-quasidiagonal quotient by the compact operators

1991 ◽  
Vol 110 (1) ◽  
pp. 143-145 ◽  
Author(s):  
Simon Wassermann
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Finite Rank ◽  
Separable Hilbert Space ◽  
Compact Operators ◽  
C Algebra ◽  
Alternative Characterization ◽  
Image Position ◽  
Algebra Of Operators

A C*-algebra A of operators on a separable Hilbert space H is said to be quasidiagonal if there is an increasing sequence E1, E2, … of finite-rank projections on H tending strongly to the identity and such thatas i → ∞ for T∈A. More generally a C*-algebra is quasidiagonal if there is a faithful *-representation π of A on a separable Hilbert space H such that π(A) is a quasidiagonal algebra of operators. When this is the case, there is a decomposition H = H1 ⊕ H2 ⊕ … where dim Hi < ∞ (i = 1, 2,…) such that each T∈π(A) can be written T = D + K where D= D1 ⊕ D2 ⊕ …, with Di∈L(Hi) (i = 1, 2,…), and K is a compact linear operator on H. As is well known (and readily seen), this is an alternative characterization of quasidiagonality.

Sign in / Sign up

Export Citation Format

Share Document