Operator theoretic properties of semigroups in terms of their generators

S. Blunck, and L. Weis. "Operator theoretic properties of semigroups in terms of their generators." Studia Mathematica 146.1 (2001): 35-54. <http://eudml.org/doc/284933>.

@article{S2001,
abstract = {Let $(T_\{t\})$ be a C₀ semigroup with generator A on a Banach space X and let be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ,A) of A belongs to if and only if the integrated semigroup $S_\{t\}: = ∫_\{0\}^\{t\} T_\{s\}ds$ belongs to . For analytic semigroups, $S_\{t\} ∈ $ implies $T_\{t\} ∈ $, and in this case we give precise estimates for the growth of the -norm of $T_\{t\}$ (e.g. the trace of $T_\{t\}$) in terms of the resolvent growth and the imbedding D(A) ↪ X.},
author = {S. Blunck, L. Weis},
journal = {Studia Mathematica},
keywords = {resolvent -semigroup; operator ideal; generator; Phillips functional calculus},
language = {eng},
number = {1},
pages = {35-54},
title = {Operator theoretic properties of semigroups in terms of their generators},
url = {http://eudml.org/doc/284933},
volume = {146},
year = {2001},
}

TY - JOUR
AU - S. Blunck
AU - L. Weis
TI - Operator theoretic properties of semigroups in terms of their generators
JO - Studia Mathematica
PY - 2001
VL - 146
IS - 1
SP - 35
EP - 54
AB - Let $(T_{t})$ be a C₀ semigroup with generator A on a Banach space X and let be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ,A) of A belongs to if and only if the integrated semigroup $S_{t}: = ∫_{0}^{t} T_{s}ds$ belongs to . For analytic semigroups, $S_{t} ∈ $ implies $T_{t} ∈ $, and in this case we give precise estimates for the growth of the -norm of $T_{t}$ (e.g. the trace of $T_{t}$) in terms of the resolvent growth and the imbedding D(A) ↪ X.
LA - eng
KW - resolvent -semigroup; operator ideal; generator; Phillips functional calculus
UR - http://eudml.org/doc/284933
ER -