Spectral Mapping Theorem for Rakocević and Schmoeger Essential Spectra of a Multivalued Linear Operator

2014 ◽  
Vol 12 (3) ◽  
pp. 1019-1031 ◽  
Author(s):  
Faiçal Abdmouleh ◽  
Teresa Àlvarez ◽  
Aymen Ammar ◽  
Aref Jeribi
Keyword(s):  
Linear Operator ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Essential Spectra ◽  
Multivalued Linear Operator

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

An unbounded spectral mapping theorem

1968 ◽  
Vol 8 (1) ◽  
pp. 119-127 ◽  
Author(s):  
S. J. Bernau
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Closed Subset ◽  
Complex Banach Space ◽  
Complex Numbers ◽  
Spectral Mapping Theorem ◽  
Complex Polynomials ◽  
Spectral Mapping ◽  
Image Position ◽  
Densely Defined

Recall that the spectrum, σ(T), of a linear operator T in a complex Banach space is the set of complex numbers λ such that T—λI does not have a densely defined bounded inverse. It is known [7, § 5.1] that σ(T) is a closed subset of the complex plane C. If T is not bounded, σ(T) may be empty or the whole of C. If σ(T) ≠ C and T is closed the spectral mapping theorem, is valid for complex polynomials p(z) [7, §5.7]. Also, if T is closed and λ ∉ σ(T), (T–λI)−1 is everywhere defined.

scholarly journals On totally paranormal operators

2002 ◽  
Vol 66 (3) ◽  
pp. 425-441 ◽  
Author(s):  
Christoph Schmoeger
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Continuous Linear Operator ◽  
Complex Banach Space ◽  
Weyl’S Theorem ◽  
Continuous Linear ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Operator Equations ◽  
Weyl Spectrum

A continuous linear operator on a complex Banach space is said to be paranormal if ‖Tx‖2 ≤ ‖T2x‖ ‖x‖ for all x ∈ X. T is called totally paranormal if T–λ is paranormal for every λ ∈ C. In this paper we investigate the class of totally paranormal operators. We shall see that Weyl's theorem holds for operators in this class. We also show that for totally paranormal operators the Weyl spectrum satisfies the spectral mapping theorem. In Section 5 of this paper we investigate the operator equations eT = eS and eTeS = eSeT for totally paranormal operators T and S.

scholarly journals A spectral mapping theorem for perturbed Ornstein–Uhlenbeck operators on L2(Rd)

2015 ◽  
Vol 268 (9) ◽  
pp. 2479-2524 ◽  
Author(s):  
Roland Donninger ◽  
Birgit Schörkhuber
Keyword(s):  
Spectral Mapping Theorem ◽  
Spectral Mapping

Joint Spectrum and the Spectral Mapping Theorem

1995 ◽  
pp. 73-80
Author(s):  
M. S. Livšic ◽  
N. Kravitsky ◽  
A. S. Markus ◽  
V. Vinnikov
Keyword(s):  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Joint Spectrum
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