References
P. Billard, S. Kwapien, A. Pelczynski, and Ch. Samuel, “Biorthogonal Systems of Random Unconditional Convergence in Banach Spaces,” In:Longhorn Notes of the University of Texas at Austin, Funct. Anal. Seminar (1985–1986).
S. Kwapien and A. Pelczynski, “The main triangle projection in matrix spaces and its application,”Studio Math.,34, 43–68 (1970).
D. R. Lewis, “An isomorphic characterization of the Schmidt class,”Compositio Math.,30, 291–297 (1970).
D. J. H. Garling and N. Tomczak-Jaegermann, “RUC-systems and Besselian systems in Banach spaces,”Math. Proc. Camb. Phil. Soc.,106, 163–169 (1989).
M. Takesaki,Theory of Operator Algebras. Vol. 1, Springer-Verlag (1979).
S. G. Krein, Yu. I. Petunin, and E. M. Semenov,Interpolation of Linear Operators [in Russian], Nauka, Moscow (1978).
J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces. I, Springer-Verlag (1977).
J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces. II, Springer-Verlag (1979).
T. Fack and H. Kosaki, “Generalizeds-numbers ofτ-measurable operators,”Pacific J. Math.,123, 269–300 (1986).
E. Nelson, “Notes on noncommutative integration,”J. Funct. Anal.,15, 103–116 (1974).
P. G. Dodds, T. R.-Y. Dodds, and B. Pagter, “Noncommutative Banach function spaces,”Math. Z.,201, 583–597 (1989).
F. A. Sukochev and V. I. Chilin,Weak convergence in noncommutative symmetric spaces, Manuscript deposited at VINITI, No. 2028-B90 (1990).
T. Fack, “Type and cotype inequalities for noncommutativeL p-spaces,”J. Operator Theory,17, 255–279 (1987).
N. Tomczak-Jaegermann, “The moduli of smoothness and convexity and the Rademacher averages of trace classesS p (1≤p<∞),”Studia Math.,50, 163–182 (1974).
F. A. Sukochev and V. I. Chilin, “Isomorphism of separable noncommutativeL p-spaces on von Neumann algebras of type 1,” In: 13-thAll Union School in the Theory of Operators in Functional Spaces, Heads of the Reports, Kuibyshev (1988), p. 180.
H. W. Ellis, “On the basis problem for vector-valued function spaces,”Can. J. Math.,8, 412–422 (1956).
A. V. Bukhvalov, “Continuity of operators in a vector-valued function space: Applications to the basis theory,”Zap. Nauchn. Sem., Leningrad. Otdel. Mat. Inst. Steklov (LOMI),157, 5–22 (1987).
Ch. A. McCarty, “C p,”Israel J. Math.,5, 249–271 (1967).
E. Berkson, Th. A. Gillespie, and P. S. Muhly, “Theorie spectrale dans les espaces UMD,”C. R. Acad. Sci. Paris Ser. I,302, No. 4, 155–158 (1986).
P. G. Dodds, T. R.-Y. Dodds, and B. Pagter, “Remarks on noncommutative interpolation,”Proc. CMACANUD,24, 58–78 (1989).
A. V. Bukhvalov, “Theorems on the interpolation of sublinear operators in mixed norm spaces,” In:Qualitative and Approximate Methods of Investigating Operator Equations, Mezhvus. Tem. Sb., Yaroslavl (1984), pp. 90–105.
Y. Berg and Y. Lefstrem,Interpolational Spaces. Introduction [Russian translation], Mir, Moscow (1980).
G. Pisier, “Types des espaces normes,”C. R. Acad. Sci. Paris, Ser. 1,276, 1673–1674 (1973).
B. S. Kashin and A. A. Saakian,Orthogonal Series [in Russian], Nauka, Moscow (1984).
A. V. Krygin,p-convexity and q-concavity of noncommutative symmetric space, Manuscript deposited at VINITI, No. 2027-B90 (1990).
J. Arazy and P.-K. Lin, “Onp-convexity andq-concavity of unitary matrix spaces,”Int. Eq. Oper.,8, 295–313 (1985).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 56, No. 1, pp. 88–104, July, 1994.
Rights and permissions
About this article
Cite this article
Sukochev, F.A. RUC-bases inE(L ∞711-01711-01711-01B(H)) andF(C E). Math Notes 56, 711–721 (1994). https://doi.org/10.1007/BF02110562
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02110562