Abstract:
Given two complex Banach spaces X1 and X2, a tensor product of X1 and X2, X1 ⊗̃ X2, in the sense of J. Eschmeier ([5]), and two finite tuples of commuting operators, S = (S1,..., Sn) and T = (T1,..., Tm), defined on X1 and X2 respectively, we consider the (n+m)-tuple of operators defined on X1 ⊗̃ X2, (S ⊗ I,I ⊗ T) = (S1 ⊗ I,..., Sn ⊗ I, I ⊗ T1,..., I ⊗ Tm), and we give a description of the semi-Browder joint spectra introduced by V. Kordula, V. Müller and V. Rakočević in [7] and of the split semi-Browder joint spectra (see Section 3) of the (n+m)-tuple (S ⊗ I, I ⊗ T), in terms of the corresponding joint spectra of S and T. This result is in some sense a generalization of a formula obtained for other various Browder spectra in Hilbert spaces and for tensor products of operators and for tuples of the form (S ⊗ I, I ⊗ T). In addition, we also describe all the mentioned joint spectra for a tuple of left and right multiplications defined on an operator ideal between Banach spaces in the sense of [5].
Registro:
| Documento: |
Artículo
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| Título: | Tensor products and the semi-browder joint spectra |
| Autor: | Boasso, E. |
| Filiación: | Departamento de Matemática, Ciudad Universitaria Pab. I, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
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| Palabras clave: | Semi-Browder and split joint spectra; Semi-Fredholm |
| Año: | 2002
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| Volumen: | 47
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| Número: | 1
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| Página de inicio: | 79
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| Página de fin: | 95
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| Título revista: | Journal of Operator Theory
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| Título revista abreviado: | J. Oper. Theory
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| ISSN: | 03794024
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v47_n1_p79_Boasso |
Referencias:
- Buoni, J.J., Harte, R., Wickstead, T., Upper and lower Fredholm spectra (1977) Proc. Amer. Math. Soc., 66, pp. 309-314
- Curto, R., Dash, A.T., Browder spectral systems (1988) Proc. Amer. Math. Soc., 103, pp. 407-413
- Dash, A.T., Joint Browder spectra and tensor products (1985) Bull. Austral. Math. Soc., 32, pp. 119-128
- Eschmeier, J., Analytic spectral mapping theorems for joint spectra (1987) Oper. Theory Adv. Appl., 24, pp. 167-181. , Birkhäuser, Basel
- Eschmeier, J., Tensor products and elementary operators (1988) J. Reine Angew. Math., 390, pp. 47-66
- Ichinose, T., Spectral properties of tensor product of linear operators. I (1978) Trans. Amer. Math. Soc., 235, pp. 75-113
- Kordula, V., Müller, V., Rakočević, V., On the semi-Browder spectrum (1997) Studia Math., 123, pp. 1-13
- Słodkowski, Z., An infinite family of joint spectra (1977) Studia Math., 61, pp. 239-255
- Taylor, J.L., A joint spectrum for several commuting operators (1970) J. Funct. Anal., 6, pp. 172-191
Citas:
---------- APA ----------
(2002)
. Tensor products and the semi-browder joint spectra. Journal of Operator Theory, 47(1), 79-95.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v47_n1_p79_Boasso [ ]
---------- CHICAGO ----------
Boasso, E.
"Tensor products and the semi-browder joint spectra"
. Journal of Operator Theory 47, no. 1
(2002) : 79-95.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v47_n1_p79_Boasso [ ]
---------- MLA ----------
Boasso, E.
"Tensor products and the semi-browder joint spectra"
. Journal of Operator Theory, vol. 47, no. 1, 2002, pp. 79-95.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v47_n1_p79_Boasso [ ]
---------- VANCOUVER ----------
Boasso, E. Tensor products and the semi-browder joint spectra. J. Oper. Theory. 2002;47(1):79-95.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03794024_v47_n1_p79_Boasso [ ]
