Abstract
Peculiar properties of hermitian and positive n-times integrated C-cosine functions on Banach spaces are investigated. Among them are: (1) Any nondegenerate positiven -times integrated C-cosine function is infinitely differentiable in operator norm; (2) An exponentially bounded, nondegenerateC -cosine function on L p(μ) (1<p<∞) (orL 1(μ), C0 , in case C has dense range) is positive if and only if its generator is bounded, positive, and commutes with C.
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Li, YC., Shaw, SY. Hermitian and Positive Integrated C-cosine Functions on Banach Spaces. Positivity 2, 281–299 (1998). https://doi.org/10.1023/A:1009724402831
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DOI: https://doi.org/10.1023/A:1009724402831