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Strictly singular embeddings

Novikov, S.Ya. and Semenov, Evgeny M. and Hernández, Francisco L. (2002) Strictly singular embeddings. Functional Analysis and its applications , 36 (1). pp. 71-73. ISSN 0016-2663

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Abstract

An operator A mapping a Banach space E into a Banach space F is called strictly singular (or Kato) if any restriction of A to an infinite-dimensional subspace of E is not an isomorphism. The paper deals with the problem of describing all couples of rearrangement-invariant spaces E↪F for which the embedding operator is strictly singular.


Item Type:Article
Uncontrolled Keywords:Rearrangement invariant Banach space; strictly singular embedding; disjointly strictly singular embedding; Rademacher system; exponential Orlicz space
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:16034
References:

J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I. Sequence Spaces, Springer-Verlag, Berlin, 1977.

A. García del Amo, F. L. Hernández, and C. Ruiz, Proc. Roy. Soc. Edinburg. Sect. A, 126, 1011–1026 (1996).

J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II. Function Spaces, Springer-Verlag, Berlin, 1979.

S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolation of Linear Operators, Moscow [in Russian], Nauka, 1978; English transl. Amer. Math. Soc., 1982.

S. Ya. Novikov, Mat. Zametki, 62, No. 4, 549–563 (1997).

A. Grothendieck, Canad. J. Math., 6, 158–160 (1954).

A. García del Amo, F. L. Hernández, V. M. Sánchez, and E. M. Semenov, J. London Math. Soc., 62, 239–252 (2000).

V. A. Rodin and E. M. Semenov, Anal. Math., 1, 207–222 (1975).

D. J. Aldous, Trans. Amer. Math. Soc., 267, 445–463 (1981).

L. Dor, Ann. of Math., 102, 463–474 (1975).

D. Dacunha-Castelle, J.-L. Krivine, Israel J. Math., 26, 330–351 (1977).

Y. Raunaud, Illinois J. Math., 39, 212–250 (1995).

S. Montgomery-Smith, E. M. Semenov, Positivity, 4, 397–402 (2000).

Tokarev E. V., Funkts. Analiz. Prilozhen., 13, No. 2, 93–94 (1979).

S. Ya. Novikov, Collect. Math., 44, 211–215 (1993).

W. B. Johnson, B. Maurey, G. Schechtman, and L. Tzafriri, Memoirs Amer. Math. Soc., 217 (1979).

M. I. Kadec and A. Pelczynski, Studia Math., 21, 161–176 (1961/1962).

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