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Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction ........................................................................................................... 5
1. Notation and definitions.......................................................................................... 7
2. Elementary properties of dilations........................................................................ 8
3. Semi-groups and their representations ............................................................. 9
4. Minimality and uniqueness of dilations............................................................... 13
5. Positive definite operator valued functions ........................................................ 17
6. General existence theorems................................................................................. 23
7. Positive definite functions on groups................................................................... 32
8. Intertwining operators for dilatable operator functions..................................... 37
9. Dilations of operator functions on star algebras................................................ 44
References.................................................................................................................... 60
Introduction ........................................................................................................... 5
1. Notation and definitions.......................................................................................... 7
2. Elementary properties of dilations........................................................................ 8
3. Semi-groups and their representations ............................................................. 9
4. Minimality and uniqueness of dilations............................................................... 13
5. Positive definite operator valued functions ........................................................ 17
6. General existence theorems................................................................................. 23
7. Positive definite functions on groups................................................................... 32
8. Intertwining operators for dilatable operator functions..................................... 37
9. Dilations of operator functions on star algebras................................................ 44
References.................................................................................................................... 60
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
153
Liczba stron
61
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLIII
Daty
wydano
1978
Twórcy
autor
Bibliografia
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- [3] M. D. Choi, Positive linear maps on C*-algebras, Canad. J. Math. 24 (1972), p. 520-529.
- [4] Ch. Davis, A Schwarz inequality for convex operator functions, Proc. Amer. Math. Soc. 8 (1957), p. 42-44.
- [5] J. Dixmier, Les C*-algèbres et leurs représentations, Paris 1964.
- [6] N. Dunford and J. T. Schwartz, Linear operators, Part II, New York-London 1963.
- [7] Ch. F. Dunkl and D. E. Ramirez, Representations of commutative semitopological semigroups, Lect. Notes, Math. 435, Berlin-Heidelberg-New York 1975.
- [8] P. Halmos, Normal dilations and extensions of operators, Summa Brasil. Math. 2 (1950), p. 125-134.
- [9] R. V. Kadison, A generalized Schwarz inequality and algebraic invariants for operator algebras, Ann. Math. 56 (1952), p. 494-503.
- [10] H. Langer, Ein Zerspaltungssatz für Operatoren in Hilbertraum, Acta Math. Hung. 12 (1961), p. 441-445.
- [11] A. Lebow, On von Neumann theory of spectral sets, J. Math. Anal. Appl. 7 (1963), p. 64-90.
- [12] R. J. Lindashl and P. H. Maserick, Positive definite functions on involution semigroups, Duke Math. J. 38, 4 (1971), p. 771-782.
- [13] P. Masani, An explicit treatment of dilation theory (preprint 1975 Aut.)
- [14] P. H. Maserick, Spectral theory of operator valued transformations, J. Math. Ann. Appl. 41, 2 (1973), p. 497-507.
- [15] W. Mlak, Unitary dilations of contraction operators, Rozprawy Mat., Warszawa 1965.
- [16] W. Mlak, A note on general dilation theorems (to appear in Banach Center Publ. Spectral Semester, fall 1977).
- [17] W. Mlak and Cz. Ryll-Nardzewski, Positive definite operator functions which are representations, Bull. Polon. Acad. Sci. 22 (1974), p. 1111-1115.
- [18] W. Mlak and W. Szymański, Dilation theorems for *-semigroups without unit (preprint).
- [19] W. Mlak and A. Weron, Dilations of Banach space operator valued functions, Ann. Polon. Math, (to appear).
- [20] M. A. Naimark, Positive definite operator functions on a commutative group, Bull. Izv. Acad. Sci. URSS sér. math. 7 (1943), p. 237-244 (Russian, with English summary).
- [21] M. A. Naimark, On a representation of additive set functions, C. R. Doklady Acad. Sci. URSS 41 (1943), p. 359-361.
- [22] M. A. Naimark, Normed rings, Groningen 1964.
- [23] J. Von Neumann, Eine Spektraltheorie fur allgemeine Operatoren eines unitären Raumes, Math. Nachr. 4 (1951), p. 258-281.
- [24] T. W. Palmer, *-representation of U*-algebras, Indiana Univ. Math. J. 20 (1971), p. 929-933.
- [25] W. L. Paschke, Completly positive maps on U*-algebras, Proc. Amer. Math. Soc. 34, 2 (1972), p. 412-416.
- [26] F. Riesz and B. Sz-Nagy, Functional analysis, New York 1955.
- [27] W. F. Stinespring, Positive functions on C*-algebras, Proc. Amer. Math. Soc. 6 (1955), p. 211-216.
- [28] E. Størmer, Positive linear maps of 0*-algebras, Lect. Notes Phys. Springer (1973).
- [29] F. H. Szafraniec, Note on a general dilation theorem, Ann. Polon. Math. 36 (to appear).
- [30] F. H. Szafraniec, On the boundedness condition involved in dilation theory, Bull. Acad. Sci. Pol. 24 (1976), p. 877-881.
- [31] F. H. Szafraniec, Dilations on involution semi-groups, Proc. Amor. Math. Soc. (to appear).
- [32] B. Sz-Nagy, Sur les contractions de l'espace de Hilbert, Acta Sci. Math. 15 (1953), p. 87-92.
- [33] B. Sz-Nagy, Transformations de l'espace de Hilbert. Fonctions de type positif sur un qroupe, ibidem 15 (1954), p. 104-114.
- [34] B. Sz-Nagy, Prolongement des transformations de l'espace de Hilbert qui sortent de cet espace, Appendix ad F. Riesz and B. Sz.-Nagy, Leçons d'analyse fonctionnelle, Budapest 1955.
- [35] B. Sz-Nagy and C. Foiaş, Sur les contractions de l'espace de Hilbert, III, Acta Sci. Math. 19 (1958), p. 26-46.
- [36] B. Sz-Nagy and C. Foiaş, Harmonic analysis of operators on Hilbert space, Budapest-Amsterdam-London 1970.
- [37] B. Sz-Nagy and A. Koranyi, Operatortheoretische Behandlung und Verallgemeinerung eines Problem Kreises in der Komplexen Funktionen theorie, Acta Math. 100 (1958), p. 171-202.
- [38] D. M. Topping, Lectures on von Neumann algebras, London-New Jork 1971.
- [39] H. Umegaki, Positive definite functions and direct product Hilbert space, Tohoku Math. J. 2, 7 (1955), p. 206-211.
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