Alvarez: Ultraweakly compact operators and dual spaces

Alvarez, Teresa:
Ultraweakly compact operators and dual spaces
Bollettino dell'Unione Matematica Italiana Serie 8 7-B (2004), fasc. n.3, p. 697-711, Unione Matematica Italiana (English)
pdf (273 Kb), djvu (211 Kb). | MR2101660 | Zbl 1179.47020

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In questo articolo si introduce e si caratterizza la classe di tutti gli operatori ultradebolmente compatti, definiti negli spazi di Banach per mezzo dei loro operatori coniugati. Si analizza la relazione esistente fra un operatore ultradebolmente compatti e il suo coniugato. Si presentano esempi di operatori appartenenti a questa classe. Inoltre, si studia la connessione fra la compattezza ultradebole di $T\in L(X, Y)$ e i sottospazi minimali di $Y'$ e si presenta un risultato relativo alla fattorizzazione degli operatori ultradebolmente compatti.

Referenze Bibliografiche

[1] T. ÁLVAREZ-V. M. ONIEVA, On operators factorizable through quasi-reflexive Banach spaces, Arch. Math. Vol., 48 (1987), 85-87. | MR 878013 | Zbl 0635.47017

[2] J. M. F. CASTILLO-M. GONZÁLEZ, Three-space Problems in Banach Space Theory (Springer Lecture Notes in Math. 1667, 1997). | MR 1482801 | Zbl 0914.46015

[3] J. R. CLARK, Coreflexive and somewhat reflexive Banach spaces, Proc. Amer. Math. Soc., 36 (1972), 421-427. | MR 308748 | Zbl 0264.46009

[4] R. W. CROSS, Multivalued linear Operators (Marcel Dekker, New York, 1998.) | MR 1631548 | Zbl 0911.47002

[5] J. DAVIS-T. FIGIEL-W. JOHNSON-A. PELCZYNSKI, Factoring weakly compact operators, J. Funct. Anal., 17 (1976), 311-327. | MR 355536 | Zbl 0306.46020

[6] J. DIXMIER, Sur un théorème de Banach, Duke Math. J. 15 (1948), 1057-1071. | fulltext mini-dml | MR 27440 | Zbl 0031.36301

[7] N. DUNFORD-J. T. SCHWARTZ, Linear Operators Part I (Interscience, New York, 1958). | Zbl 0084.10402

[8] D. VAN DULST, Ultra weak topologies on Banach spaces, Proc. of the seminar on random series, convex sets and geometry of Banach spaces, Various Publ. Series, 24 (1975), 57-66. | MR 390724 | Zbl 0319.46010

[9] D. VANDULST, Reflexive and superreflexiveBanach spaces (Mathematisch Centrum, Amsterdam, 1978). | MR 513590 | Zbl 0412.46006

[10] G. GODOFREY, Espaces de Banach: Existence et unicité de certains préduax, Ann. Inst. Fourier, Grenoble, no. 3 (1978). | MR 511815 | Zbl 0368.46015

[11] S. GOLDBERG, Unbounded Linear Operators (McGraw-Hill, New York, 1966). | MR 200692 | Zbl 0148.12501

[12] M. GONZÁLEZ-V. M. ONIEVA, Semi-Fredholm operators and semigroups associated with some classical operator ideals, Proc. Royal Irish Acad., Ser. A, 88A (1988), 35-38. | MR 974281 | Zbl 0633.47029

[13] R. C. JAMES, Some self-dual properties of normed linear spaces, Ann. of Math. Studies, 69 (1972), 159-175. | MR 454600 | Zbl 0233.46025

[14] N. I. KALTON-A. PELCZYNSKI, Kernels of surjections from $L_1$-spaces with an applications to Sidon sets, Math. Ann. 309, no. 1 (1997), 135-158. | MR 1467651 | Zbl 0901.46008

[15] J. LINDENSTRAUSS-L. TZAFRIRI, Classical Banach spaces I, sequence spaces (Springer-Verlag, New York, 1997). | MR 500056 | Zbl 0362.46013

[16] R. D. NEIDINGER, Properties of Tauberian Operators on Banach Spaces (Doctoral dissertation, University of Texas at Austin, 1984).

[17] M. I. OSTROVSKI, Total subspaces in dual Banach spaces which are not norming over any infinite dimensional subspace, Studia Math., 105 (1993), 37-49. | fulltext mini-dml | MR 1222187 | Zbl 0810.46016

[18] H. P. ROSENTHAL, On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from $L^p(\mu)$ to $L^r(\mu)$, J. Funct. Anal., 4 (1969), 176-214. | MR 250036 | Zbl 0185.20303

[19] K. W. YANG, The generalized Fredholm operators, Trans. Amer. Math. Soc., 216 (1976), 313-326. | MR 423114 | Zbl 0297.47027

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Referenze Bibliografiche