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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
0. Introduction...............................................5
1. Preliminaries.............................................6
2. Power series space-valued case..............8
3. Main results..............................................9
4. F- and DF-subspaces.............................11
5. Quasidiagonal isomorphism....................13
6. Sufficiency...............................................14
7. Linear Topological Invariants (LTI)..........16
8. Necessary conditions..............................20
9. Spaces $s ⊗̂ E'_∞(b)$............................22
10. Spaces $s' ⊗̂ E_{∞}(a)$.......................23
References.................................................26
0. Introduction...............................................5
1. Preliminaries.............................................6
2. Power series space-valued case..............8
3. Main results..............................................9
4. F- and DF-subspaces.............................11
5. Quasidiagonal isomorphism....................13
6. Sufficiency...............................................14
7. Linear Topological Invariants (LTI)..........16
8. Necessary conditions..............................20
9. Spaces $s ⊗̂ E'_∞(b)$............................22
10. Spaces $s' ⊗̂ E_{∞}(a)$.......................23
References.................................................26
Słowa kluczowe
Tematy
Kategoryzacja MSC:
- 46A04: Locally convex Fr\'echet spaces and (DF)-spaces
- 46A32: Spaces of linear operators; topological tensor products; approximation properties
- 46A45: Sequence spaces (including K\"othe sequence spaces)
- 46A11: Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
350
Liczba stron
27
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCL
Daty
wydano
1996
otrzymano
1995-03-2
poprawiono
1995-05-09
Twórcy
autor
- Department of Mathematics, Bilkent University, 06533 Ankara, Turkey
- State Building Academy, Rostov-on-Don, Russia
autor
- Department of Mathematics, Marmara Research Center, Gebze-Kocaeli, Turkey
- Department of Mechanics and Mathematics, Rostov State University, Rostov-on-Don, Russia
autor
- Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Bibliografia
- [1] A. Aytuna, J. Krone and T. Terzioğlu, Complemented infinite type power series subspaces of nuclear spaces, Math. Ann. 283 (1989), 193-202.
- [2] V. I. Baran, On quasiequivalence of absolute bases in Cartesian products of Köthe spaces, in: Actual Problems of Mathematical Analysis, Rostov-on-Don, 1978, 13-21 (in Russian).
- [3] C. Bessaga, Some remarks on Dragilev's theorem, Studia Math. 31 (1968), 307-318.
- [4] C. Bessaga, A. Pełczyński and S. Rolewicz, On diametral approximative dimension and linear homogeneity of F-spaces, Bull. Acad. Polon. Sci. 9 (1961), 677-683.
- [5] P. A. Chalov and V. P. Zahariuta, On linear topological invariants, manuscript No. 5941-85, deposited at VINITI, 1985 (in Russian).
- [6] P. A. Chalov and V. P. Zahariuta, On linear topological invariants on some class of families of Hilbert spaces, manuscript No. 3862-B 86, deposited at VINITI, 1986 (in Russian).
- [7] M. M. Dragilev, On regular bases in nuclear spaces, Mat. Sb. 68 (1965), 153-173 (in Russian).
- [8] M. M. Dragilev, On special dimensions, defined on some classes of Köthe spaces, Mat. Sb. 80 (1969), 225-240 (in Russian).
- [9] M. M. Dragilev, Bases in Köthe spaces, Rostov State Univ., Rostov-on-Don, 1983 (in Russian).
- [10] E. Dubinsky, The structure of Nuclear Fréchet Spaces, Lecture Notes in Math. 720, Springer, 1979.
- [11] E. Dubinsky and D. Vogt, Bases in complemented subspaces of power series spaces, Bull. Polish Acad. Sci. 34 (1986), 65-67.
- [12] A. Goncharov, T. Terzioğlu and V. Zahariuta, On isomorphic classification of spaces $s ⊗̂ E'_∞(a)$, in: Linear Topological Spaces and Complex Analysis, METU-TÜBİTAK, Ankara, 1994, 14-24.
- [13] A. P. Goncharov and V. P. Zahariuta, Linear topological invariants for tensor products of power F-, DF-spaces, Turkish J. Math. 1 (1995), 90-101.
- [14] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
- [15] A. N. Kolmogorov, On the linear dimension of topological vector spaces, Dokl. Akad. Nauk SSSR 120 (1958), 239-241 (in Russian).
- [16] V. P. Kondakov, Questions of geometry of non-normed spaces, Rostov State Univ., Rostov-on-Don, 1983 (in Russian).
- [17] B. S. Mityagin, Approximative dimension and bases in nuclear spaces, Uspekhi Mat. Nauk 16 (4) (1961), 63-132 (in Russian).
- [18] B. S. Mityagin, Equivalence of bases in Hilbert scales, Studia Math. 37 (1971), 111-137 (in Russian).
- [19] B. S. Mityagin, Non-Schwartzian power series spaces, Math. Z. 182 (1983), 303-310.
- [20] A. Pełczyński, On the approximation of S-spaces by finite-dimensional spaces, Bull. Acad. Polon. Sci. 5 (1957), 879-881.
- [21] H. H. Schaefer, Topological Vector Spaces, Grad. Texts in Math. 3, Springer, New York, 1971.
- [22] T. Terzioğlu, Some invariants of Fréchet spaces and imbeddings of smooth sequence spaces, in: Advances in the Theory of Fréchet Spaces, Kluwer, 1989, 305-324.
- [23] M. Valdivia, Topics in Locally Convex Spaces, North-Holland Math. Stud. 67, North-Holland, Amsterdam, 1982.
- [24] D. Vogt, Charakterisierung der Unterräume von s, Math. Z. 155 (1977), 109-117.
- [25] D. Vogt, Eine Charakterisierung der Potenzreihenräume von endlichem Typ und ihre Folgerungen, Manuscripta Math. 37 (1982), 269-301.
- [26] V. P. Zahariuta, Linear topological invariants and isomorphisms of spaces of analytic functions, Mat. Anal. i Prilozhen., Rostov Univ., 2 (1970), 3-13; 3 (1971), 176-180 (in Russian).
- [27] V. P. Zahariuta, Some linear topological invariants and isomorphisms of tensor products of scale's centers, Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauk. 4 (1974), 62-64 (in Russian).
- [28] V. P. Zahariuta, On isomorphisms and quasiequivalence of bases of power Köthe spaces, Dokl. Akad. Nauk SSSR 221 (1975), 772-774 (in Russian).
- [29] V. P. Zahariuta, On isomorphisms and quasiequivalence of bases of power Köthe spaces, in: Proc. 7th Winter School in Drogobych, 1976, 101-126 (in Russian).
- [30] V. P. Zahariuta, Generalized Mityagin invariants and continuum pairwise nonisomorphic spaces of analytic functions, Funktsional. Anal. i Prilozhen. 11 (3) (1977), 24-30 (in Russian).
- [31] V. P. Zahariuta, Synthetic diameters and linear topological invariants, in: School on Theory of Operators in Function Spaces (Abstracts of Reports), Minsk, 1978, 51-52 (in Russian).
- [32] V. P. Zahariuta, Isomorphism of spaces of vector-valued infinitely differentiable functions, in: School on Theory of Operators in Function Spaces (Abstracts of Reports), Minsk, 1982 (in Russian).
- [33] V. P. Zahariuta, On isomorphic classification of F-spaces, in: Lecture Notes in Math. 1043, Springer, 1984, 34-37.
- [34] V. P. Zahariuta, Linear topological invariants and their applications to generalized power spaces, manuscript of survey, Rostov State Univ., 1979 (in Russian); revised English version will appear in Turkish J. Math.
- [35] V. P. Zahariuta, Linear topological invariants and mixed (F,DF)-spaces, Mathematische Forschungsinstitut Oberwolfach, Tagungsbericht 44/1992, Funktionalanalysis (4.10-10.10.1992), 21.
Języki publikacji
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Uwagi
1991 Mathematics Subject Classification: 46A04, 46A45, 46A11, 46A32.
Identyfikator YADDA
bwmeta1.element.zamlynska-6c2c543e-4209-46fe-9868-b7f372fc924b
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
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