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Boolean algebras of projections and ranges of spectral measures

Seria
Rozprawy Matematyczne tom/nr w serii: 365 wydano: 1997
Zawartość
Warianty tytułu
Abstrakty
EN
CONTENTS
Introduction...............................................................................5
1. Preliminaries.........................................................................7
2. Relative weak compactness of the range............................13
3. Closed spectral measures...................................................16
4. Spectral measures and B.a.'s of projections........................22
References..............................................................................45
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 365
Liczba stron
33
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCLXV
Daty
wydano
1997
otrzymano
1996-04-09
Twórcy
autor
  • Unit 3, 77 Nightcliff Road, Nightcliff, N.T. 0810, Australia
autor
Bibliografia
  • [1] W. G. Bade, On Boolean algebras of projections and algebras of operators, Trans. Amer. Math. Soc. 80 (1955), 345-359.
  • [2] W. G. Bade, A multiplicity theory for Boolean algebras of projections in Banach spaces, Trans. Amer. Math. Soc. 92 (1959), 508-530.
  • [3] P. G. Dodds and B. de Pagter, Orthomorphisms and Boolean algebras of projections, Math. Z. 187 (1984), 361-381.
  • [4] P. G. Dodds and B. de Pagter, Algebras of unbounded scalar-type spectral operators, Pacific J. Math. 130 (1987), 41-74.
  • [5] P. G. Dodds and B. de Pagter and W. J. Ricker, Reflexivity and order properties of scalar-type spectral operators in locally convex spaces, Trans. Amer. Math. Soc. 293 (1986), 355-380.
  • [6] P. G. Dodds and W. J. Ricker, Spectral measures and the Bade reflexivity theorem, J. Funct. Anal. 61 (1985), 136-163.
  • [7] N. Dunford and J. T. Schwartz, Linear Operators III. Spectral Operators, Wiley-Interscience, New York, 1971.
  • [8] H. Dye, The unitary structure in finite rings of operators, Duke Math. J. 20 (1953), 55-70.
  • [9] C. K. Fong and L. Lam, On spectral theory and convexity, Trans. Amer. Math. Soc. 264 (1981), 59-75.
  • [10] T. A. Gillespie, Spectral measures on spaces not containing $l^{∞}$, Proc. Edinburgh Math. Soc. 24 (1981), 41-45.
  • [11] A. Grothendieck, Produits tensoriels et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  • [12] J. Hoffmann-Jørgensen, Vector measures, Math. Scand. 28 (1971), 5-32.
  • [13] I. Kluvánek, Conical measures and vector measures, Ann. Inst. Fourier (Grenoble) 27 (1977), 83-105.
  • [14] I. Kluvánek and G. Knowles, Vector Measures and Control Systems, North-Holland, Amsterdam, 1976.
  • [15] G. Köthe, Topological Vector Spaces I, Springer, Heidelberg, 1969.
  • [16] I. Labuda, A note on exhaustive measures, Comment. Math. Prace Mat. 18 (1975), 217-221.
  • [17] W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam, 1971.
  • [18] B. Nagy, On Boolean algebras of projections and prespectral operators, in: Oper. Theory Adv. Appl. 6, Birkhäuser, Basel, 1982, 145-162.
  • [19] S. Okada and W. J. Ricker, Spectral measures which fail to be equicontinuous, Period. Math. Hungar. 28 (1994), 55-61.
  • [20] S. Okada and W. J. Ricker, Vector measures and integration in non-complete spaces, Arch. Math. (Basel) 63 (1994), 344-353.
  • [21] S. Okada and W. J. Ricker, The range of the integration map of a vector measure, Arch. Math. (Basel) 64 (1995), 512-522.
  • [22] S. Okada and W. J. Ricker, Continuous extensions of spectral measures, Colloq. Math. 71 (1996), 115-132.
  • [23] S. Okada and W. J. Ricker, Spectral measures and automatic continuity, Bull. Belg. Math. Soc. Simon Stevin 3 (1996), 267-279.
  • [24] W. J. Ricker, On Boolean algebras of projections and scalar-type spectral operators, Proc. Amer. Math. Soc. 87 (1983), 73-77.
  • [25] W. J. Ricker, Countable additivity of multiplicative, operator-valued set functions, Acta Math. Hungar. 47 (1986), 121-126.
  • [26] W. J. Ricker, Remarks on completeness in spaces of linear operators, Bull. Austral. Math. Soc. 34 (1986), 25-35.
  • [27] W. J. Ricker, Boolean algebras of projections of uniform multiplicity one, in: Proc. Centre Math. Anal. Austral. Nat. Univ. 24, Austral. Nat. Univ., Canberra, 1989, 206-212.
  • [28] W. J. Ricker, Completeness of the L¹-space of closed vector measures, Proc. Edinburgh Math. Soc. 33 (1990), 71-78.
  • [29] W. J. Ricker, Boolean algebras of projections and spectral measures in dual spaces, in: Oper. Theory Adv. Appl. 43, Birkhäuser, Basel, 1990, 289-300.
  • [30] W. J. Ricker, Weak compactness in spaces of linear operators, in: Proc. Centre Math. Anal. Austral. Nat. Univ. 29, Austral. Nat. Univ., Canberra, 1992, 212-221.
  • [31] W. J. Ricker, Spectral measures, boundedly σ-complete Boolean algebras and applications to operator theory, Trans. Amer. Math. Soc. 304 (1987), 819-838.
  • [32] W. J. Ricker, Criteria for closedness of vector measures, Proc. Amer. Math. Soc. 91 (1984), 75-80.
  • [33] I. Tweddle, Weak compactness in locally convex spaces, Glasgow Math. J. 9 (1968), 123-127.
  • [34] B. Walsh, Structure of spectral measures on locally convex spaces, Trans. Amer. Math. Soc. 120 (1965), 295-326.
  • [35] B. Walsh, Spectral decomposition of quasi-Montel spaces, Proc. Amer. Math. Soc. 17 (1966), 1267-1271.
Języki publikacji
EN
Uwagi
1991 Mathematics Subject Classification: 47B15, 47D30.
Identyfikator YADDA
bwmeta1.element.zamlynska-1add9905-19f0-4020-b4ec-a5fb4b404973
Identyfikatory
ISSN
0012-3862
Kolekcja
DML-PL
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