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## Studia Mathematica

1995 | 113 | 3 | 283-298
Tytuł artykułu

### Adjoint characterisations of unbounded weakly compact, weakly completely continuous and unconditionally converging operators

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Characterisations are obtained for the following classes of unbounded linear operators between normed spaces: weakly compact, weakly completely continuous, and unconditionally converging operators. Examples of closed unbounded operators belonging to these classes are exhibited. A sufficient condition is obtained for the weak compactness of T' to imply that of T.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
283-298
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-11-08
poprawiono
1994-12-08
Twórcy
autor
• Department of Mathematics, University of Oviedo, 33007 Oviedo, Spain
autor
• Department of Mathematics, University of Cape Town, 7700 Rondebosch, South Africa
autor
• Department of Mathematics, University of Cape Town, 7700 Rondebosch, South Africa
Bibliografia
• [AO] T. Alvarez and V. Onieva, A note on three-space ideals of Banach spaces, in: Proccedings of the Tenth Spanish-Portuguese Conference on Mathematics, III (Murcia, 1985), Univ. Murcia, Murcia, 1985, 251-254.
• [BKS] V. I. Bogachev, B. Kirchheim and W. Schachermeyer, Continuous restrictions of linear maps between Banach spaces, Acta Univ. Carolin.-Math. Phys. 30 (2) (1989), 31-35.
• [C1] R. W. Cross, Properties of some norm related functions of unbounded linear operators, Math. Z. 199 (1988), 285-302.
• [C2] R. W. Cross, Unbounded linear operators of upper semi-Fredholm type in normed spaces, Portugal. Math. 47 (1990), 61-79.
• [C3] R. W. Cross, $F_+$-operators are Tauberian, Quaestiones Math. 16 (1993), 129-132.
• [C4] R. W. Cross, Note on some characterisations of unbounded weakly compact operators, ibid., to appear.
• [C5] R. W. Cross, Linear transformations of Tauberian type in normed spaces, Note Mat. 10 (1990), Suppl. No. 1, 193-203 (volume dedicated to the memory of Professor Gottfried M. Köthe).
• [C6] R. W. Cross, On a theorem of Kalton and Wilansky concerning Tauberian operators, J. Math. Anal. Appl. 171 (1992), 156-170.
• [C7] R. W. Cross, Adjoints of non-densely defined linear operators, in: Aportaciones Mat., volume dedicated to the memory of Prof. Victor Onieva, Univ. Cantabria, Santander, 1991, 117-136.
• [CL1] R. W. Cross and L. E. Labuschagne, Partially continuous and semi-continuous linear operators in normed spaces, Exposition. Math. 7 (1989), 189-191.
• [CL2] R. W. Cross and L. E. Labuschagne, Characterisations of operators of lower semi-Fredholm type in normed spaces, Quaestiones Math. 15 (1992), 151-173.
• [D] J. Dixmier, Sur un théorème de Banach, Duke Math. J. 15 (1948), 1057-1071.
• [DS] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958.
• [F] V. Fonf, Private communication.
• [G] S. Goldberg, Unbounded Linear Operators, McGraw-Hill, New York, 1966.
• [Gv] A. I. Gouveia, Unbounded linear operators in seminormed spaces, Univ. Cape Town Thesis Reprints 9/1990.
• [HM] J. Howard and K. Melendez, Characterizing operators by their first and second adjoint, Bull. Inst. Math. Acad. Sinica 5 (1977), 129-134.
• [K] G. Köthe, General linear transformation of locally convex spaces, Math. Ann. 159 (1965), 309-328.
• [L] L. E. Labuschagne, Characterisations of partially continuous, strictly cosingular and $ϕ_-$ type operators, Glasgow Math. J. 33 (1991), 203-212.
• [LT] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Vol. I, Ergeb. Math. Grenzgeb. 92, Springer, 1977.
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Bibliografia
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