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On operator ranges.(English)Zbl 0224.47009


MSC:

47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
47A15 Invariant subspaces of linear operators
47A10 Spectrum, resolvent

Cite

References:

[1]Anderson, W. N.; Duffin, R. J., Series and parallel addition of matrices, J. Math. Anal. Appl., 26, 576-594 (1969) ·Zbl 0177.04904
[2]Banach, S., Théorie des Opérations Linéaires (1955), Chelsea: Chelsea Cambridge, Mass. ·Zbl 0067.08902
[3]Davis, C., Separation of two linear subspaces, Acta Sci. Math. (Szeged), 19, 172-187 (1958) ·Zbl 0090.32603
[4]de Branges, L.; Rovnyak, J., Square Summable Power Series (1966), Holt, Rinehart, and Winston: Holt, Rinehart, and Winston New York ·Zbl 0153.39603
[5]Dixmier, J., Étude sur les variétés et les opérateurs de Julia, Bull. Soc. Math. France, 77, 11-101 (1949) ·Zbl 0045.39102
[6]Dixmier, J., Sur les variétés \(J\) d’un espace de Hilbert, J. Math. Pures Appl., 28, 321-358 (1949) ·Zbl 0045.39103
[7]Dixmier, J., Position relative de deux variétés linéaires fermées dans un espace de Hilbert, Rev. Sci., 86, 387-399 (1948) ·Zbl 0031.36201
[8]Douglas, R. G., On majorization, factorization and range inclusion of operators in Hilbert space, (Proc. Amer. Math. Soc., 17 (1966)), 413-416 ·Zbl 0146.12503
[9]Erdös, P.; Shapiro, H.; Shields, A., Large and small subspaces of Hilbert space, Michigan Math. J., 12, 169-178 (1965) ·Zbl 0132.34902
[10]Fillmore, P. A., On sums of projections, J. Functional Analysis, 4, 146-152 (1969) ·Zbl 0176.43404
[11]Foiaş, C., Invariant semi-closed subspaces (1970), Institute of Mathematics: Institute of Mathematics New York, preprint
[12]Gustafson, K.; Ramsay, A., On domains of unbounded operators (1970), University of Colorado: University of Colorado Bucarest, Romania, preprint
[13]Halmos, P. R., A Hilbert Space Problem Book (1967), Van Nostrand: Van Nostrand Boulder, Colorado ·Zbl 0144.38704
[14]Heinz, E., Beiträge zur Störungstheorie der Spektralzerlegung, Math. Ann., 123, 415-438 (1951) ·Zbl 0043.32603
[15]Kaplansky, I., Functional Analysis, Some Aspects of Analysis and Probability (1958), Wiley: Wiley Princeton, N. J.
[16]Köthe, G., Das Trägheitsgesetz der quadratischen Formen im Hilbertschen Raum, Math. Z., 41, 137-152 (1936) ·JFM 62.0454.03
[17]Köthe, G., Die Gleichungstheorie im Hilbertschen Raum, Math. Z., 41, 153-162 (1936) ·JFM 62.0454.02
[18]Mackey, G. W., On the domains of closed linear transformations in Hilbert space, Bull. Amer. Math. Soc., 52, 1009 (1946)
[19]Murray, F. J., On complementary manifolds and projections in spaces\(L_p\) and\(l_p\), Trans. Amer. Math. Soc., 41, 138-152 (1937) ·Zbl 0016.21406
[20]von Neumann, J., Zur Theorie des Unbeschränkten Matrizen, J. Reine Angew. Math., 161, 208-236 (1929) ·JFM 55.0825.01
[21]Riesz, F.; Sz.-Nagy, B., Functional Analysis (1955), Ungar: Ungar New York
[22]Ryser, H. J., Combinatorial Mathematics (1963), Wiley: Wiley New York ·Zbl 0112.24806
[23]Shmulyan, Yu. L., Two-sided division in a ring of operators, Math. Notes, 1, 400-403 (1967)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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