Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras

Given two complex Banach spaces X1 and X2, a tensor product X1 ⊕ X2 of X1 and X2 in the sense of [14], two complex solvable finite-dimensional Lie algebras L1 and L2, and two representations of δ{turned}i: Li → L(Xi) of the algebras, i = 1;2, we consider the Lie algebra L = L1 L2 and the tensor prod...

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Autor principal: Boasso, E.
Formato: JOUR
Materias:
Słodkowski
Split and Fredholm joint spectra
Taylor
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00123862_v_n416_p5_Boasso
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00123862_v_n416_p5_Boasso2023-10-03T14:10:23Z Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras Boasso, E. Słodkowski Split and Fredholm joint spectra Taylor Given two complex Banach spaces X1 and X2, a tensor product X1 ⊕ X2 of X1 and X2 in the sense of [14], two complex solvable finite-dimensional Lie algebras L1 and L2, and two representations of δ{turned}i: Li → L(Xi) of the algebras, i = 1;2, we consider the Lie algebra L = L1 L2 and the tensor product representation of L, δ{turned}: L → L(X1 ⊕ X2), δ{turned} = δ{turned}1 I + I δ{turned}2. We study the Słodkowski and split joint spectra of the representation δ{turned}, and we describe them in terms of the corresponding joint spectra of δ{turned}1 and δ{turned}2. Moreover, we study the essential Słodkowski and essential split joint spectra of the representation δ{turned}, and we describe them by means of the corresponding joint spectra and essential joint spectra of δ{turned}1 and δ{turned}2. In addition, using similar arguments we describe all the above-mentioned joint spectra for the multiplication representation in an operator ideal between Banach spaces in the sense of [14]. Finally, we consider nilpotent systems of operators, in particular commutative, and we apply our descriptions to them. © Instytut Matematyczny PAN, Warszawa 2003. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00123862_v_n416_p5_Boasso
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Słodkowski
Split and Fredholm joint spectra
Taylor
spellingShingle Słodkowski
Split and Fredholm joint spectra
Taylor
Boasso, E.
Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras
topic_facet Słodkowski
Split and Fredholm joint spectra
Taylor
description Given two complex Banach spaces X1 and X2, a tensor product X1 ⊕ X2 of X1 and X2 in the sense of [14], two complex solvable finite-dimensional Lie algebras L1 and L2, and two representations of δ{turned}i: Li → L(Xi) of the algebras, i = 1;2, we consider the Lie algebra L = L1 L2 and the tensor product representation of L, δ{turned}: L → L(X1 ⊕ X2), δ{turned} = δ{turned}1 I + I δ{turned}2. We study the Słodkowski and split joint spectra of the representation δ{turned}, and we describe them in terms of the corresponding joint spectra of δ{turned}1 and δ{turned}2. Moreover, we study the essential Słodkowski and essential split joint spectra of the representation δ{turned}, and we describe them by means of the corresponding joint spectra and essential joint spectra of δ{turned}1 and δ{turned}2. In addition, using similar arguments we describe all the above-mentioned joint spectra for the multiplication representation in an operator ideal between Banach spaces in the sense of [14]. Finally, we consider nilpotent systems of operators, in particular commutative, and we apply our descriptions to them. © Instytut Matematyczny PAN, Warszawa 2003.
format JOUR
author Boasso, E.
author_facet Boasso, E.
author_sort Boasso, E.
title Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras
title_short Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras
title_full Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras
title_fullStr Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras
title_full_unstemmed Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras
title_sort joint spectra of the tensor product representation of the direct sum of two solvable lie algebras
url http://hdl.handle.net/20.500.12110/paper_00123862_v_n416_p5_Boasso
work_keys_str_mv AT boassoe jointspectraofthetensorproductrepresentationofthedirectsumoftwosolvableliealgebras
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