Abstract
The multiplicative spectrum of a complex Banach space X is the class K(X) of all (automatically compact and Hausdorff) topological spaces appearing as spectra of Banach algebras (X,*) for all possible continuous
multiplications on X turning X into a commutative
associative complex algebra with the unity. The properties of the multiplicative spectrum are studied. In particular, we show that K(X^n) consists of countable compact spaces with at most n non-isolated points for any separable hereditarily indecomposable Banach space X. We prove that K(C[0,1]) coincides with the class of all metrizable compact spaces.
Original language | English |
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Pages (from-to) | 6112-6119 |
Number of pages | 8 |
Journal | Journal of Mathematical Sciences |
Volume | 131 |
Issue number | 6 |
Publication status | Published - Dec 2005 |
ASJC Scopus subject areas
- General Mathematics