Liu Ni
Abstract
Let T be a complex decomposable bounded linear operator on Hilbert space,T-U|T| be its polar decomposition,then T,T=|T|1/2U|T|1/2 and T(*)=|T*|1/2U|T*|1/2 all have the same nonzero Kato spectrum;T and T(*) have the same reduced point spectrum.
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Let T be a complex decomposable bounded linear operator on Hilbert space,T-U|T| be its polar decomposition,then T,T=|T|1/2U|T|1/2 and T(*)=|T*|1/2U|T*|1/2 all have the same nonzero Kato spectrum;T and T(*) have the same reduced point spectrum.
Key concepts: Polar decomposition, Spectrum (functional analysis), Mathematics, Bounded operator, Hilbert space, Operator (biology), Bounded function, Pure mathematics