Abstract
We consider the propagator of an evolution equation, which is a semigroup of linear operators. Questions related to its operator norm function and its behavior at the critical point for norm continuity or compactness or differentiability are studied.
Highlights
As it is well known, each well-posed Cauchy problem for first-order evolution equation in Banach spaces u t Au t, t ≥ 0, 1.1 u 0 u0 gives rise to a well-defined propagator, which is a semigroup of linear operators, and the theory of semigroups of linear operators on Banach spaces has developed quite rapidly since the discovery of the generation theorem by Hille and Yosida in 1948
Suppose that τ0 is the critical point of the norm continuity compactness, differentiability of the operator semigroup T t t≥0
The critical point for compactness and norm continuity is τ0 0
Summary
Questions related to its operator norm function and its behavior at the critical point for norm continuity or compactness or differentiability are studied
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