A Sufficient Condition for the Similarity of a Polynomially Bounded Operator to a Contraction
نویسندگان
چکیده
منابع مشابه
A Polynomially Bounded Operator on Hilbert Space Which Is Not Similar to a Contraction
Let ε > 0. We prove that there exists an operator Tε : `2 → `2such that for any polynomial P we have ‖P (Tε)‖ ≤ (1 +ε)‖P‖∞, but Tε isnot similar to a contraction, i.e. there does not exist an invertible operatorS : `2 → `2 such that‖S−1TεS‖ ≤ 1. This answers negatively a question at-tributed to Halmos after his well-known 1970 paper (“Ten problems in Hilbertspace”). ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2018
ISSN: 1072-3374,1573-8795
DOI: 10.1007/s10958-018-4007-6