Affiliation:
1. Department of Mathematics , University of Delhi , Delhi - 110007 , India
Abstract
Abstract
In this paper, we show that the spectral mapping theorem holds for
(
m
,
n
)
*
{(m,n)^{*}}
-paranormal operators. We also exhibit the self-adjointness of the Riesz idempotent
E
λ
{E_{\lambda}}
of
(
m
,
n
)
*
{(m,n)^{*}}
-paranormal operators concerning for each isolated point λ of
σ
(
T
)
{\sigma(T)}
.
Moreover, we show Weyl’s theorem for
(
m
,
n
)
*
{(m,n)^{*}}
-paranormal operators and
f
(
T
)
{f(T)}
for every
f
∈
ℋ
(
σ
(
T
)
)
{f\in\mathcal{H}(\sigma(T))}
. Furthermore, we investigate the class of totally
(
m
,
n
)
*
{(m,n)^{*}}
-paranormal operators and show that Weyl’s theorem holds for operators in this class.
Subject
Statistics and Probability,Analysis
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