TY - JOUR
T1 - The Hille-Yosida space of an arbitrary operator
AU - Kantorovitz, Shmuel
PY - 1988/11/15
Y1 - 1988/11/15
N2 - Let A be an arbitrary Banach space operator with resolvent defined for all λ > 0. We define a linear manifold Z in the given space and a norm {triple vertical-rule fence}·{triple vertical-rule fence} on Z majorizing the given norm, such that (Z, {triple vertical-rule fence}·{triple vertical-rule fence}) is a Banach space, and the restriction of A to Z generates a strongly continuous semigroup of contractions in Z. This so-called Hille-Yosida space (Z, {triple vertical-rule fence}·{triple vertical-rule fence}) is "maximal-unique" in a suitable sense.
AB - Let A be an arbitrary Banach space operator with resolvent defined for all λ > 0. We define a linear manifold Z in the given space and a norm {triple vertical-rule fence}·{triple vertical-rule fence} on Z majorizing the given norm, such that (Z, {triple vertical-rule fence}·{triple vertical-rule fence}) is a Banach space, and the restriction of A to Z generates a strongly continuous semigroup of contractions in Z. This so-called Hille-Yosida space (Z, {triple vertical-rule fence}·{triple vertical-rule fence}) is "maximal-unique" in a suitable sense.
UR - http://www.scopus.com/inward/record.url?scp=0000722013&partnerID=8YFLogxK
U2 - 10.1016/0022-247X(88)90118-7
DO - 10.1016/0022-247X(88)90118-7
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SN - 0022-247X
VL - 136
SP - 107
EP - 111
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -