Pacific Journal of Mathematics

Weak and strong limits of spectral operators.

William G. Bade

Article information

Source
Pacific J. Math. Volume 4, Number 3 (1954), 393-413.

Dates
First available in Project Euclid: 14 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1103044796

Zentralblatt MATH identifier
0056.34802

Mathematical Reviews number (MathSciNet)
MR0063567

Subjects
Primary: 46.3X

Citation

Bade, William G. Weak and strong limits of spectral operators. Pacific J. Math. 4 (1954), no. 3, 393--413. http://projecteuclid.org/euclid.pjm/1103044796.


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References

  • [1] L. Alaoglu, Weak topologiesof normed linear spaces, Ann. of Math. 41 (1940), 252-267.
  • [2] P. Alexandroff and H. Hopf, Topologie I, Berlin, 1935.
  • [3] J. Y. Barry, On the convergenceof ordered sets of projections,Proc. Amer. Math. Soc. 5(1954), 313-314.
  • [4] J. Dieudonne', Sur le Theoreme de Hahn-Banach, Revue Sci. 79 (1941), 642-643.
  • [5] J. Dixmier, Les fonetionnelieslineares sur I'ensemble des operateurs homes d'un espace de Hubert, Ann. of Math. 51 (1950), 387-408.
  • [6] J. Dixmier, Sur certains espaces consideres par M. H. Stone, Summa Brasiliensis Mathematicae 2(1951), 151-182.
  • [7] N. Dunford, Direct decomposition of Banach spaces, Boletin de la Sociedad Matematica Mexicana 3 (1946), 1-12.
  • [8] N. Dunford, Spectral theory II. Resolutions of the identity, Pacific J. Math. 2 (1952), 559-614.
  • [9] N. Dunford,Spectral operators, Pacific J. Math. 4 (1954), 321-354.
  • [10] J. M. G. Fell and J. L. Kelley, An algebra of unbounded operators, Proc. Nat. Acad. Sci. 38 (1952), 592-598.
  • [11] I. Gelfand, Normierte Ringe, Rec. Math. (Math. Sbornik) N.S. 9 (1941), 3-24.
  • [12] F. Hartogs, and A. Rosenthal, Uber Folgen analytischer Funktionen. {Erganzung zur Arbeit im 100. Band), Math. Ann. 104 (1931), 606-610.
  • [13] S. Kakutani, An example concerning uniform boundedness of spectralmeasures. Pacific J. Math. 4 (1954), 363-372.
  • [14] I. Kaplansky, A theorem on rings of operators, Pacific J. Math. 1 (1951), 227-232.
  • [15] J. L. Kelley, Convergence in topology, Duke Math. J. 17(1950), 277-284.
  • [16] M. Lavrentieff, Sur les functionsdyune variable complexe representables par des series de polynomes, Actualite's Sci. Ind. 441, Paris, 1936.
  • [17] E. R. Lorch, On a calculus of operators in reflexive vector spaces, Trans. Amer. Math. Soc. 45(1939), 217-234.
  • [18] S. Mergelyan, On the representationof functions by series of polynomials on closedsets,Doklady Akad. Nauk SSSR (N.S.) 78 (1951), 405-408. [Amer. Math. Soc. Translation No.85.]
  • [19] E. A. Michael, Transformations from a linear space with weak topology, Proc. Amer. Math. Soc. 3 (1952), 671-676.
  • [20] B.v.Sz. Nagy, Spektraldarstellunglinearer Transformationen desHilbertschen Raumes, Berlin, 1942.
  • [21] F. Rellich, Storungstheorieder SpektralzerlegungII, Math. Ann. 113 (1936), 667-685.
  • [22] I.E. Segal, Decomposition of operator algebras II: Multiplicity theory, Mem. Amer. Math. Soc. 9 (1951).
  • [23] M.H. Stone, Linear transformations in Hubert space and their applicationsto analysis, Amer. Math. Soc. Coll. Publications, vol. 15, New York, 1932.
  • [24] M.H. Stone, A general theory of spectra I, Proc. Nat. Acad. Sci. 27 (1941), 83-87.
  • [25] M.H. Stone, The generalized Weierstrass approximation theorem, Math. Mag. 21 (1948), 167-184, 237-254.
  • [26] M.H. Stone, Boundednessproperties in function-lattices,Canadian J. of Math. 1 (1949), 176-186.
  • [27] J. von Neumann, Zur Algebra der Funktionaloperatoren und Theorie der normalen Operatoren, Math. Ann. 102(1929), 370-427.