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

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

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 -