Schur Algebras overC*-Algebras
2007 ◽
Vol 2007
◽
pp. 1-15
Keyword(s):
Let𝒜be aC*-algebra with identity1, and lets(𝒜)denote the set of all states on𝒜. Forp,q,r∈[1,∞), denote by𝒮r(𝒜)the set of all infinite matricesA=[ajk]j,k=1∞over𝒜such that the matrix(ϕ[A[2]])[r]:=[(ϕ(ajk*ajk))r]j,k=1∞defines a bounded linear operator fromℓptoℓqfor allϕ∈s(𝒜). Then𝒮r(𝒜)is a Banach algebra with the Schur product operation and norm‖A‖=sup{‖(ϕ[A[2]])r‖1/(2r):ϕ∈s(𝒜)}. Analogs of Schatten's theorems on dualities among the compact operators, the trace-class operators, and all the bounded operators on a Hilbert space are proved.
2005 ◽
Vol 2005
(14)
◽
pp. 2175-2193
◽
Keyword(s):
Keyword(s):
1989 ◽
Vol 32
(3)
◽
pp. 320-326
◽
1969 ◽
Vol 21
◽
pp. 1421-1426
◽
2020 ◽
Vol 18
(05)
◽
pp. 2050031
Keyword(s):
2008 ◽
Vol 39
(4)
◽
pp. 347-352
◽
1971 ◽
Vol 23
(1)
◽
pp. 132-150
◽