Tensor products and the semi-browder joint spectra
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...
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_03794024_v47_n1_p79_Boasso |
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| Sumario: | 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]. |
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