×

zbMATH — the first resource for mathematics

On Boolean algebras of projections and algebras of operators. (English) Zbl 0066.36202

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] William G. Bade, Weak and strong limits of spectral operators, Pacific J. Math. 4 (1954), 393 – 413. · Zbl 0056.34802
[2] R. G. Bartle, N. Dunford, and J. Schwartz, Weak compactness and vector measures, Canad. J. Math. 7 (1955), 289 – 305. · Zbl 0068.09301
[3] Mahlon Day M., Ergodic theorems for Abelian semigroups, Trans. Amer. Math. Soc. 51 (1942), 399 – 412. · Zbl 0063.01057
[4] Mahlon M. Day, Means for the bounded functions and ergodicity of the bounded representations of semi-groups, Trans. Amer. Math. Soc. 69 (1950), 276 – 291. · Zbl 0039.12301
[5] J. Dixmier, Sur certains espaces considérés par M. H. Stone, Summa Brasil. Math. 2 (1951), 151 – 182 (French). · Zbl 0045.38002
[6] Nelson Dunford, Direct decompositions of Banach spaces, Bol. Soc. Mat. Mexicana 3 (1946), 1 – 12. · Zbl 0061.25205
[7] Nelson Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321 – 354. · Zbl 0056.34601
[8] Nelson Dunford, Spectral theory. II. Resolutions of the identity, Pacific J. Math. 2 (1952), 559 – 614. · Zbl 0047.35903
[9] H. A. Dye, The unitary structure in finite rings of operators, Duke Math. J. 20 (1953), 55 – 69. · Zbl 0050.11405
[10] J. M. G. Fell and J. L. Kelley, An algebra of unbounded operators, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 592 – 598. · Zbl 0049.20701
[11] J. L. Kelley, Convergence in topology, Duke Math. J. 17 (1950), 277 – 283. · Zbl 0038.27003
[12] Kiyonori Kunisawa, Some theorems on abstractly-valued functions in an abstract space, Proc. Imp. Acad. Tokyo 16 (1940), 68 – 72. · Zbl 0023.13002
[13] Edgar R. Lorch, On a calculus of operators in reflexive vector spaces, Trans. Amer. Math. Soc. 45 (1939), no. 2, 217 – 234. · Zbl 0020.30701
[14] E. R. Lorch, Bicontinuous linear transformations in certain vector spaces, Bull. Amer. Math. Soc. 45 (1939), 564 – 569. · Zbl 0022.05302
[15] G. W. Mackey, Commutative Banach algebras, multigraphed Harvard lecture notes, ed. by A. Blair, 1952. · Zbl 0086.31203
[16] Béla de Sz. Nagy, On uniformly bounded linear transformations in Hilbert space, Acta Univ. Szeged. Sect. Sci. Math. 11 (1947), 152 – 157. · Zbl 0029.30501
[17] B. J. Pettis, Absolutely continuous functions in vector spaces, Bull. Amer. Math. Soc. Abstract 45-9-360.
[18] F. Riesz, Sur les fonctions des transformations hermitiennes dans l’espace de Hilbert, Acta Univ. Szeged vol. 7 (1935) pp. 147-159. · Zbl 0012.02204
[19] Andrew Sobczyk, Projection of the space (\?) on its subspace (\?\(_{0}\)), Bull. Amer. Math. Soc. 47 (1941), 938 – 947. · Zbl 0027.40801
[20] M. H. Stone, Boundedness properties in function-lattices, Canadian J. Math. 1 (1949), 176 – 186. · Zbl 0032.16901
[21] John Wermer, Commuting spectral measures on Hilbert space, Pacific J. Math. 4 (1954), 355 – 361. · Zbl 0056.34701
[22] F. Wolf, Simplicity of spectra in general operators, Bull. Amer. Math. Soc. Abstract 60-4-428.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.