Examples discussion 11
نویسنده
چکیده
[11.1] For T : V → V a continuous (=bounded) linear map of a Banach space V to itself, show that the operator norm is an upper bound for absolute values of all eigenvalues λ: |λ|C ≤ |T |op. Further, show that |T |op is an upper bound for all of the spectrum, that is, T − λ is invertible for |λ|C > |T |op. Discussion: First, for Tv = λ · v for 0 6= v ∈ V , without loss of generality take |v| = 1, and then
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تاریخ انتشار 2017