More on the ‘‘zero-two” law
نویسندگان
چکیده
منابع مشابه
Zero-two law for cosine families
For (C(t))t≥0 being a strongly continuous cosine family on a Banach space, we show that the estimate lim supt→0+ ‖C(t) − I‖ < 2 implies that C(t) converges to I in the operator norm. This implication has become known as the zero-two law. We further prove that the stronger assumption of supt≥0 ‖C(t) − I‖ < 2 yields that C(t) = I for all t ≥ 0. For discrete cosine families, the assumption supn∈N ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1976
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1976-0428076-2