Author:
Touré Cheick,Brits Rudi,Sebastian Geethika
Abstract
Abstract
We present here a multiplicative version of the classical Kowalski–Słodkowski theorem, which identifies the characters among the collection of all functionals on a complex and unital Banach algebra A. In particular, we show that, if A is a
$C^\star $
-algebra, and if
$\phi :A\to \mathbb C $
is a continuous function satisfying
$ \phi (x)\phi (y) \in \sigma (xy) $
for all
$x,y\in A$
(where
$\sigma $
denotes the spectrum), then either
$\phi $
is a character of A or
$-\phi $
is a character of A.
Publisher
Canadian Mathematical Society
Cited by
3 articles.
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