Abstract
It is known [2] that a Banach algebra А generated by 2N idempotents with relations (1), (2) is an algebra with matrix symbol of order 2N. This symbol is completely and explicitly defined via the spectrums of two (indicator) elements (3) and (5). But in the case when А is a c*-algebra, the symbol constructed in [2] is notsymmetric. Moreover in order to construct asymmetric symbol, one needs some additional information about the algebra А, even for the case whenp j=p *j (j=1, ..., 2N). These additional conditions and the explicit form ofsymmetric symbol are described in this paper.
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Krupnik, N. Symmetrization of the symbol in Banach algebras generated by idempotents. Integr equ oper theory 31, 470–481 (1998). https://doi.org/10.1007/BF01228103
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DOI: https://doi.org/10.1007/BF01228103