Journal of Operator Theory
Volume 47, Issue 1, Winter 2002 pp. 79-95.
Tensor products and the semi-Browder joint spectraAuthors: Enrico Boasso
Author institution: Departamento de Matematica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria Pab. I, 1428 Buenos Aires, Argentina
Summary: 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 seeSection3 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].
Keywords: Semi-Fredholm, semi-Browder and split joint spectra
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