# Norm continuity of ${c}_{0}$-semigroups

Studia Mathematica (1999)

- Volume: 134, Issue: 2, page 169-178
- ISSN: 0039-3223

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topGoersmeyer, V., and Weis, L.. "Norm continuity of $c_0$-semigroups." Studia Mathematica 134.2 (1999): 169-178. <http://eudml.org/doc/216630>.

@article{Goersmeyer1999,

abstract = {We show that a positive semigroup $T_t$ on $L_p(Ω,ν)$ with generator A and ||R(α + i β)|| → 0 as |β| → ∞ for some α ∈ ℝ is continuous in the operator norm for t>0. The proof is based on a criterion for norm continuity in terms of “smoothing properties” of certain convolution operators on general Banach spaces and an extrapolation result for the $L_p$-scale, which may be of independent interest.},

author = {Goersmeyer, V., Weis, L.},

journal = {Studia Mathematica},

keywords = {convolution operators; norm continuity of a -semigroup; spaces of -integrable functions; asymptotic behaviour of the resolvent of the generator},

language = {eng},

number = {2},

pages = {169-178},

title = {Norm continuity of $c_0$-semigroups},

url = {http://eudml.org/doc/216630},

volume = {134},

year = {1999},

}

TY - JOUR

AU - Goersmeyer, V.

AU - Weis, L.

TI - Norm continuity of $c_0$-semigroups

JO - Studia Mathematica

PY - 1999

VL - 134

IS - 2

SP - 169

EP - 178

AB - We show that a positive semigroup $T_t$ on $L_p(Ω,ν)$ with generator A and ||R(α + i β)|| → 0 as |β| → ∞ for some α ∈ ℝ is continuous in the operator norm for t>0. The proof is based on a criterion for norm continuity in terms of “smoothing properties” of certain convolution operators on general Banach spaces and an extrapolation result for the $L_p$-scale, which may be of independent interest.

LA - eng

KW - convolution operators; norm continuity of a -semigroup; spaces of -integrable functions; asymptotic behaviour of the resolvent of the generator

UR - http://eudml.org/doc/216630

ER -

## References

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