TY  - JOUR
T1  - On norm-preserving isomorphisms of $L^{p}(\mu,H)$
AU  - Güntürk, B.a.
AU  - Cengiz, B.
AU  - Gürdal, M.
PY  - 2016
DA  - February
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 33
EP  - 41
VL  - 45
IS  - 1
LA  - en
AB  - Given an arbitrary positive measure space $(X,A,\mu)$ and a Hilbert space $H$.In this article we give a new proof for the characterization theorem of the surjective linear isometries of the space$L^{p}(\mu,H)$ (for $1\leq p<\infty$, $p\neq 2$)which is essentially different from the existing one, and depends on the p-projections of$L^{p}(\mu,H)$.We generalize the known characterization of the p-projections of$L^{p}(\mu,H)$ for $\sigma$-finitemeasure to the arbitrary case. They are proved to be the multiplication operations by the characteristic functions of the locally measurable sets, or that of the clopen (closed-open) subsets of the hyperstonean space the measure $\mu$ determines.
KW  - Measure space
KW  - Bochner space
KW  - perfect measure
KW  - hyperstonean space
KW  - linear isometries
CR  - ...
UR  - https://dergipark.org.tr/en/pub/hujms/article/524263
L1  - https://dergipark.org.tr/en/download/article-file/644627
ER  -