On 𝑝-𝐶* summing operators

Nowak, Krzysztof

doi:10.1090/S0002-9939-1991-1034881-2

On $p$-$C^ *$ summing operators
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by Krzysztof Nowak PDF

Proc. Amer. Math. Soc. 111 (1991), 657-662 Request permission

Abstract:

We prove that every bounded linear operator $T:A \to {C_p}(H)$ such that $i \circ T:A \to B(H)$ is positive (where $A$ is a unital ${C^*}$-algebra, ${C_p}(H)$ a Schatten class, $i$ the identity map from ${C_p}(H)$ into $B(H)$ is $p - {C^*}$ summing. This permits us to characterize $p - {C^*}$ summing operators in some classes of multipliers.

References

William B. Arveson, Subalgebras of $C^{\ast }$-algebras, Acta Math. 123 (1969), 141–224. MR 253059, DOI 10.1007/BF02392388
G. Bennett, Schur multipliers, Duke Math. J. 44 (1977), no. 3, 603–639. MR 493490
B. Russo and H. A. Dye, A note on unitary operators in $C^{\ast }$-algebras, Duke Math. J. 33 (1966), 413–416. MR 193530
Uffe Haagerup, The Grothendieck inequality for bilinear forms on $C^\ast$-algebras, Adv. in Math. 56 (1985), no. 2, 93–116. MR 788936, DOI 10.1016/0001-8708(85)90026-X
Gilles Pisier, Grothendieck’s theorem for noncommutative $C^{\ast }$-algebras, with an appendix on Grothendieck’s constants, J. Functional Analysis 29 (1978), no. 3, 397–415. MR 512252, DOI 10.1016/0022-1236(78)90038-1
Robert Schatten, Norm ideals of completely continuous operators, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 27, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0119112
Barry Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge-New York, 1979. MR 541149