scholarly journals Ascent, essential ascent, descent and essential descent for a linear relation in a linear space

Filomat ◽  
2017 ◽  
Vol 31 (3) ◽  
pp. 709-721 ◽  
Author(s):  
Ezzeddine Chafai ◽  
Tereza Álvarez
Keyword(s):  
Linear Space ◽  
Linear Relation ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping

For a linear relation in a linear space some spectra defined by means of ascent, essential ascent, descent and essential descent are introduced and studied. We prove that the algebraic ascent, essential ascent, descent and essential descent spectrum of a linear relation in a linear space satisfy the polynomial spectral mapping theorem. As an application of the obtained results we show that the topological ascent, essential ascent, descent and essential descent spectrum verify the polynomial spectral mapping theorem.

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

scholarly journals A spectral mapping theorem for semigroups solving PDEs with nonautonomous past

2003 ◽  
Vol 2003 (16) ◽  
pp. 933-951 ◽  
Author(s):  
Genni Fragnelli
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Partial Differential ◽  
The Stability

We prove a spectral mapping theorem for semigroups solving partial differential equations with nonautonomous past. This theorem is then used to give spectral conditions for the stability of the solutions of the equations.

scholarly journals The spectrum of orthogonal sums of subnormal pairs

1988 ◽  
Vol 30 (1) ◽  
pp. 11-15 ◽  
Author(s):  
K. Rudol
Keyword(s):  
Invariant Subspace ◽  
Spectral Theory ◽  
Existence And Uniqueness ◽  
Normal Extension ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Basic Properties ◽  
Subspace Theorem ◽  
Subnormal Operators ◽  
Minimal Normal Extension

This note provides yet another example of the difficulties that arise when one wants to extend the spectral theory of subnormal operators to subnormal tuples. Several basic properties of a subnormal operator Y remain true for tuples; e.g. the existence and uniqueness of its minimal normal extension N, the spectral inclusion σ(N)⊂ σ(Y)-proved for n-tuples in [4] and generalized to infinite tuples in [5]. However, neither the invariant subspace theorem nor the spectral mapping theorem in the “strong form” as in [3] is known so far for subnormal tuples.

Two "Generic" Proofs of the Spectral Mapping Theorem

2004 ◽  
Vol 111 (7) ◽  
pp. 572 ◽  
Author(s):  
Torsten Ekedahl ◽  
Dan Laksov
Keyword(s):  
Spectral Mapping Theorem ◽  
Spectral Mapping
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