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$${\mathfrak A}$$-spectral dilations for operators on Banach spaces. (English) Zbl 0242.47014

##### MSC:
 47A20 Dilations, extensions, compressions of linear operators 47B40 Spectral operators, decomposable operators, well-bounded operators, etc. 47A65 Structure theory of linear operators
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##### References:
 [1] Bishop, E., Spectral theory for operators on a Banach space, Trans. amer. math. soc., 86, 414-445, (1957) · Zbl 0080.09903 [2] Chevalley, Cl., () [3] Colojoarǎ, I.; Foiaş, C., Theory of generalized spectral operators, (1969), Gordon and Breach, Sci. Publ New York [4] Dunford, N., Spectral operators, Pacific. J. math., 4, 21-354, (1954) · Zbl 0056.34601 [5] Tulcea, C.Ionescu, Scalar dilations and scalar extensions of operators on Banach spaces (I), J. math. mech., 14, 841-865, (1965) · Zbl 0138.39203 [6] Tulcea, C.Ionescu; Plafker, S., Dilatations et extensions scalaires sur LES espaces de Banach, C. R. acad. sci. Paris, 265, 734-735, (1967) · Zbl 0177.41103 [7] Maeda, F.-Y., Generalized spectral operators on locally convex spaces, Pacific J. math., 13, 177-192, (1963) · Zbl 0137.32003 [8] Plafker, S., Generalized subscalar operators on Banach spaces, J. math. anal. appl., 24, 345-361, (1968) · Zbl 0187.06404 [9] Rota, C.G., Multiplicative extensions of positive linear operators, Notices amer. math. soc., 8, 272-273, (1961) [10] Stroescu, E., $$U$$-scalar dilations and $$U$$-scalar extensions of operators on Banach spaces, Rev. roumaine math. pures appl., XVI, 567-572, (1969) · Zbl 0186.45401 [11] Stroescu, F., Unele proprietăţati spectrale ale operatorilor-subscalari, Studii şi cercetări matematice, 22, no. 1, 81-85, (1970) [12] Storescu, E., $$A$$-spectral representations, Rev. roumaine math. pures appl., XIV, 1207-1211, (1969) [13] Stroescu, E., $$a$$-spectral transformations on locally convex spaces, Rev. roumaine math. pures appl., XV, 701-712, (1970) [14] Yosida, K., Functional analysis, (1965), Springer-Verlag Berlin · Zbl 0126.11504
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