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Abstract:

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.

Registro:

Documento: Artículo
Título:Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras
Autor:Boasso, E.
Filiación:Departamento de Matemática, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, (1428) Buenos Aires, Argentina
Palabras clave:Słodkowski; Split and Fredholm joint spectra; Taylor
Año:2003
Número:416
Página de inicio:5
Página de fin:46
DOI: http://dx.doi.org/10.4064/dm416-0-1
Título revista:Dissertationes Mathematicae
Título revista abreviado:Diss. Math.
ISSN:00123862
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00123862_v_n416_p5_Boasso

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Citas:

---------- APA ----------
(2003) . Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras. Dissertationes Mathematicae(416), 5-46.
http://dx.doi.org/10.4064/dm416-0-1
---------- CHICAGO ----------
Boasso, E. "Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras" . Dissertationes Mathematicae, no. 416 (2003) : 5-46.
http://dx.doi.org/10.4064/dm416-0-1
---------- MLA ----------
Boasso, E. "Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras" . Dissertationes Mathematicae, no. 416, 2003, pp. 5-46.
http://dx.doi.org/10.4064/dm416-0-1
---------- VANCOUVER ----------
Boasso, E. Joint spectra of the tensor product representation of the direct sum of two solvable Lie algebras. Diss. Math. 2003(416):5-46.
http://dx.doi.org/10.4064/dm416-0-1