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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction..............................................................................................5
I. Basic definitions and notation..............................................................6
M-bases and finite-dimensional decompositions....................................6
Some geometric properties of Banach spaces.......................................9
II. Constructions of equivalent norms.....................................................12
III. (p,q)-estimates in interpolation spaces..............................................21
IV. Geometric properties of operators....................................................26
Nearly uniformly convex operators........................................................27
Nearly uniformly smooth operators.........................................................30
V. Factoring operators through nearly uniformly convex spaces...........35
Factorizations and geometric properties of operators..........................35
The case of spaces with finite-dimensional decompositions.................40
References.............................................................................................45
Introduction..............................................................................................5
I. Basic definitions and notation..............................................................6
M-bases and finite-dimensional decompositions....................................6
Some geometric properties of Banach spaces.......................................9
II. Constructions of equivalent norms.....................................................12
III. (p,q)-estimates in interpolation spaces..............................................21
IV. Geometric properties of operators....................................................26
Nearly uniformly convex operators........................................................27
Nearly uniformly smooth operators.........................................................30
V. Factoring operators through nearly uniformly convex spaces...........35
Factorizations and geometric properties of operators..........................35
The case of spaces with finite-dimensional decompositions.................40
References.............................................................................................45
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
363
Liczba stron
46
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXIII
Daty
wydano
1997
otrzymano
1994-09-26
poprawiono
1996-11-08
Twórcy
autor
- Department of Mathematics, Maria Curie-Skłodowska University, 20-031 Lublin, Poland
Bibliografia
- [1] J. Banaś, On modulus of noncompact convexity and its properties, Canad. Math. Bull. 30 (1987), 186-192.
- [2] J. Banaś, Compactness conditions in the geometric theory of Banach spaces, Nonlinear Anal. 16 (1991), 669-682.
- [3] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980.
- [4] B. Beauzamy, Propriétés géométriques des espaces d'interpolation, Exposé 14, Sém. Maurey Schwartz, École Polytechnique, Paris, 1974/75.
- [5] B. Beauzamy, Opérateurs uniformément convexifiants, Studia Math. 57 (1976), 103-159.
- [6] B. Beauzamy, Banach-Saks properties and spreading models, Math. Scand. 44 (1979), 357-384.
- [7] J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, New York, 1976.
- [8] S. Byrd, Factoring operators satisfying p-estimates, Trans. Amer. Math. Soc. 310 (1988), 567-582.
- [9] J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414.
- [10] W. J. Davis, T. Figiel, W. B. Johnson and A. Pełczyński, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327.
- [11] J. Diestel, Geometry of Banach Spaces - Selected Topics, Springer, New York, 1975.
- [12] J. Diestel, Sequences and Series in Banach Spaces, Springer, New York, 1984.
- [13] N. Dunford and J. T. Schwartz, Linear Operators I, Interscience, New York, 1958.
- [14] P. Enflo, Banach spaces which can be given an equivalent uniformly convex norm, Israel J. Math. 13 (1973), 281-288.
- [15] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Univ. Press, Cambridge, 1990.
- [16] K. Goebel and T. Sękowski, The modulus of noncompact convexity, Ann. Univ. Mariae Curie-Skłodowska Sect. A 38 (1984), 41-48.
- [17] V. I. Gurariĭ and N. I. Gurariĭ, On bases in uniformly convex and uniformly smooth Banach spaces, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 210-215 (in Russian).
- [18] E. Hille and R. S. Phillips, Functional Analysis and Semi-groups, Amer. Math. Soc. Providence, R.I., 1957.
- [19] R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 743-749.
- [20] V. I. Istrăţescu, Strict Convexity and Complex Strict Convexity. Theory and Applications, Lecture Notes in Pure Appl. Math. 89, Marcel Dekker, New York, 1984.
- [21] R. C. James, Weak compactness and reflexivity, Israel J. Math. 80 (1964), 542-550.
- [22] R. C. James, Super-reflexive spaces with bases, Pacific J. Math. 41 (1972), 409-419.
- [23] K. John and V. Zizler, Smoothness and its equivalents in weakly compactly generated Banach spaces, J. Funct. Anal. 15 (1974), 1-11.
- [24] W. B. Johnson, Factoring compact operators, Israel J. Math. 9 (1971), 337-345.
- [25] W. B. Johnson, On quotients of Lₚ which are quotients of lₚ, Compositio Math. 33 (1976), 69-89.
- [26] D. Kutzarova, L. Nikolova and S. Prus, Infinite dimensional geometric properties of real interpolation spaces, preprint.
- [27] D. Kutzarova and S. Prus, Operators which factor through nearly uniformly convex spaces, Boll. Un. Mat. Ital. B (7) 9 (1995), 479-494.
- [28] D. Kutzarova, S. Prus and B. Sims, Remarks on orthogonal convexity of Banach spaces, Houston J. Math. 19 (1993), 603-614.
- [29] T. C. Lim, On some $L^p$ inequalities in best approximation theory, J. Math. Anal. Appl. 154 (1991), 523-528.
- [30] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I. Sequence Spaces, Springer, New York, 1977.
- [31] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II. Function Spaces, Springer, New York, 1979.
- [32] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.
- [33] G. Pisier, Martingales with values in uniformly convex spaces, Israel J. Math. 20 (1975), 326-350.
- [34] S. Prus, Nearly uniformly smooth Banach spaces, Boll. Un. Mat. Ital. B (7) 3 (1989), 507-521.
- [35] S. Prus, Banach spaces with the uniform Opial property, Nonlinear Anal. 18 (1992), 697-704.
- [36] S. Prus, Przestrzenie Banacha i operatory niemal jednostajnie wypukłe [Banach spaces and nearly uniformly convex operators], Wydawnictwo UMCS, Lublin, 1993 (in Polish).
- [37] S. Prus, On the modulus of noncompact convexity of a Banach space, Arch. Math. (Basel) 63 (1994), 441-448.
- [38] F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. 30 (1929), 264-286.
- [39] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
- [40] R. Smarzewski, On an inequality of Bynum and Drew, J. Math. Anal. Appl. 150 (1990), 146-150.
- [41] V. L. Shmulyan [V. L. Shmul'yan], Sur la structure de la sphère unitaire dans l'espace de Banach, Mat. Sb. 9 (1941), 545-561.
- [42] H. Triebel, Interpolation Theory. Function Spaces. Differential Operators, Deutscher Verlag Wiss., Berlin, 1977.
Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: 46B03, 46B10, 46B70, 47A05.
Identyfikator YADDA
bwmeta1.element.zamlynska-27804d1b-c88a-4147-b07e-8252e9f4ac7f
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
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