On an estimate for the norm of a function of a quasihermitian operator

Tom 103 / 1992

M. I. Gil Studia Mathematica 103 (1992), 17-24 DOI: 10.4064/sm-103-1-17-24

Streszczenie

Let A be a closed linear operator acting in a separable Hilbert space. Denote by co(A) the closed convex hull of the spectrum of A. An estimate for the norm of f(A) is obtained under the following conditions: f is a holomorphic function in a neighbourhood of co(A), and for some integer p the operator $A^p - (A*)^p$ is Hilbert-Schmidt. The estimate improves one by I. Gelfand and G. Shilov.

Autorzy

  • M. I. Gil

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