(p, q; r)-absolutely summing operators

Ken-ichi MIYAZAKI

doi:10.2969/jmsj/02420341

(p, q; r)-absolutely summing operators

Ken-ichi MIYAZAKI

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1972 Volume 24 Issue 2 Pages 341-354

DOI https://doi.org/10.2969/jmsj/02420341

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Published: 1972 Received: October 21, 1971 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Dunford and J. T. Schwartz, Linear operators I, II, New York, 1958, 1963.
2) I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfad-joint operators, Moscow, 1965 (Russian).
3) P. Grisvard, Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures Appl., 45 (1966), 143-290.
4) S. Kwapien, Some remarks on (p, q)-absolutely summing operators in l_p-spaces, Studia Math., 29 (1968), 327-337.
5) J. Lindenstrauss and A. Pelczynski, Absolutely summing operators in L_p-spaces and their applications, Studia Math., 29 (1968), 275-326.
6) J. L. Lions et J. Peetre, Sur une classe d'espaces d'interpolation, Publ. Math. de I. H. E. S., Paris, 19 (1964), 5-68.
7) B. Mitjagin and A. Pelczynski, Nuclear operators and approximative dimension, Proc. I. C. M., Moscow, (1966), 366-372.
8) K. Miyazaki, Some remarks on intermediate spaces, Bull. Kyushu Inst. Tech., 15 (1968), 1-23.
9) K. Miyazaki, Interpolation theory for Banach spaces of (p, q; r)-absolutely summing operators, to appear.
10) A. Pelczynski, A characterization of Hilbert-Schmidt operators, Studia Math., 28 (1967), 355-360.
11) A. Pietsch, Nukleare lokalkonvexe Räume, Berlin, 1965.
12) A. Pietsch, Absolut p-summierende Abbildungen in normierten Räumen, Studia Math., 28 (1967), 333-353.
13) A. Pietsch und H. Triebel, Interpolationstheorie für Banachideale von besch-ränkten linearen Operatoren, Studia Math., 29 (1968), 95-109.
14) H. Triebel, Über die Verteilung des Approximationszahlen kompakter Operatoren in Sobolev-Besov-Räumen, Invent. Math., 4 (1967), 275-293.
15) N. Tomczak, A remark on (s, t)-absolutely summing operators in L_p-spaces, Studia Math., 35 (1970), 97-100.

Right : [1] N. Dunford and J. T. Schwartz, Linear operators I, II, New York, 1958, 1963.
[2] I. C. Gohberg and M. G. Krein, Introduction to the theory of linear nonselfad-joint operators, Moscow, 1965 (Russian).
[3] P. Grisvard, Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures Appl., 45 (1966), 143-290.
[4] S. Kwapien, Some remarks on (p, q)-absolutely summing operators in l_p-spaces, Studia Math., 29 (1968), 327-337.
[5] J. Lindenstrauss and A. Pelczynski, Absolutely summing operators in L_p-spaces and their applications, Studia Math., 29 (1968), 275-326.
[6] J. L. Lions et J. Peetre, Sur une classe d'espaces d'interpolation, Publ. Math. de I. H. E. S., Paris, 19 (1964), 5-68.
[7] B. Mitjagin and A. Pelczynski, Nuclear operators and approximative dimension, Proc. I. C. M., Moscow, (1966), 366-372.
[8] K. Miyazaki, Some remarks on intermediate spaces, Bull. Kyushu Inst. Tech., 15 (1968), 1-23.
[9] K. Miyazaki, Interpolation theory for Banach spaces of (p, q; r)-absolutely summing operators, to appear.
[10] A. Pelczynski, A characterization of Hilbert-Schmidt operators, Studia Math., 28 (1967), 355-360.
[11] A. Pietsch, Nukleare lokalkonvexe Räume, Berlin, 1965.
[12] A. Pietsch, Absolut p-summierende Abbildungen in normierten Räumen, Studia Math., 28 (1967), 333-353.
[13] A. Pietsch und H. Triebel, Interpolationstheorie für Banachideale von besch-ränkten linearen Operatoren, Studia Math., 29 (1968), 95-109.
[14] H. Triebel, Über die Verteilung des Approximationszahlen kompakter Operatoren in Sobolev-Besov-Räumen, Invent. Math., 4 (1967), 275-293.
[15] N. Tomczak, A remark on (s, t)-absolutely summing operators in L_p-spaces, Studia Math., 35 (1970), 97-100.

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