Abstract. In this paper we study a conjugation on a Banach space $\x $ and show properties of operators concerning conjugation $C$ and show spectral properties of such operators. Next we show spectral properties of an $(m,C)$-symmetry (isometry) operator $T$ on a complex Banach space $\x $. We prove that, for a $C$-doubly commuting pair $(T,S)$, if $T$ is an $(m,C)$-symmetry (isometry) and $S$ is an $(n,C)$-symmetry (isometry), then $T + S$ and $TS$ are $(m + n - 1,C)$-symmetries (isometries).
DOI: 10.14232/actasm-018-801-y
AMS Subject Classification
(1991): 47A05; 47B25, 47B99
Keyword(s):
Banach space,
linear operator,
conjugation,
spectrum
Received June 4, 2018 and in final form August 31, 2018. (Registered under 51/2018.)
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