Let H be a complex infinite dimensional Hilbert space and $T\in B(H)$. Is it true that $T=I$ given $ \sigma_{p}(T)=\lbrace 1\rbrace$?
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Sahiba Arora
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Does this answer your question Compact sets as point spectrum of a bounded operator? – PinkyWay Jun 06 '20 at 12:24
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my question is for an operator T in B(H) in general, not in the case $B(H)=l_{2}$. – TryingToLearn Jun 06 '20 at 13:28
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You should edit your question and add context. – PinkyWay Jun 08 '20 at 10:04