On p-approximation properties for p-operator spaces
This paper has a two-fold purpose. Let 1 < p < ∞ . We first introduce the p-operator space injective tensor product and study various properties related to this tensor product, including the p-operator space approximation property, for p-operator spaces on L p -spaces. We then apply these prop...
Saved in:
Published in | Journal of functional analysis Vol. 259; no. 4; pp. 933 - 974 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.08.2010
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | This paper has a two-fold purpose. Let
1
<
p
<
∞
. We first introduce the
p-operator space injective tensor product and study various properties related to this tensor product, including the
p-operator space approximation property, for
p-operator spaces on
L
p
-spaces. We then apply these properties to the study of the pseudofunction algebra
PF
p
(
G
)
, the pseudomeasure algebra
PM
p
(
G
)
, and the Figà–Talamanca–Herz algebra
A
p
(
G
)
of a locally compact group
G. We show that if
G is a discrete group, then most of approximation properties for the reduced group C
∗-algebra
C
λ
∗
(
G
)
, the group von Neumann algebra
VN
(
G
)
, and the Fourier algebra
A
(
G
)
(related to amenability, weak amenability, and approximation property of
G) have the natural
p-analogues for
PF
p
(
G
)
,
PM
p
(
G
)
, and
A
p
(
G
)
, respectively. The
p-completely bounded multiplier algebra
M
cb
A
p
(
G
)
plays an important role in this work. |
---|---|
ISSN: | 0022-1236 1096-0783 |
DOI: | 10.1016/j.jfa.2010.04.007 |