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Functions and derivations of \(C^*\)-algebras. (English) Zbl 0391.46045


MSC:

46L05 General theory of \(C^*\)-algebras
47C10 Linear operators in \({}^*\)-algebras
47A60 Functional calculus for linear operators
47B39 Linear difference operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
47B47 Commutators, derivations, elementary operators, etc.
Full Text: DOI

References:

[1] Bratteli, O.; Robinson, D. W., Unbounded derivations of \(C^∗\)-algebras, I, Comm. Math. Phys., 42, 253-268 (1975) · Zbl 0302.46043
[2] Bratteli, O.; Robinson, D. W., Unbounded derivations of \(C^∗\)-algebras, II, Comm. Math. Phys., 46, 11-30 (1976) · Zbl 0315.46053
[3] Chi, D. P., Derivations in \(C^∗\)-algebras (1976), University of Pennsylvania, preprint
[4] Colojoarǎ, I.; Foiaş, C., Theory of Generalized Spectral Operators (1968), Gordon & Breach: Gordon & Breach New York · Zbl 0189.44201
[5] Kahan, W., Every \(n\) × \(n\) matrix Z with real spectrum satisfies \(∥ Z − Z^∗∥ ⩽ ∥ Z + Z^∗\) ∥ ( log2 n + 0.038)\), (Proc. Amer. Math. Soc., 39 (1973)), 235-241 · Zbl 0258.15013
[6] Kahan, W., Spectra of nearly hermitian matrices, (Proc. Amer. Math. Soc., 48 (1975)), 11-17 · Zbl 0322.15022
[7] Kantorovitz, S., Classification of operators by means of their operational calculus, Trans. Amer. Math. Soc., 115, 192-214 (1965) · Zbl 0127.07801
[8] Kato, T., Continuity of the map \(S → ¦S¦\) for linear operators, (Proc. Japan Acad., 49 (1973)), 157-160 · Zbl 0301.47006
[9] Kato, T., Perturbation Theory for Linear Operators (1966), Springer-Verlag: Springer-Verlag New York · Zbl 0148.12601
[10] McIntosh, A., Counterexample to a question on commutators, (Proc. Amer. Math. Soc., 29 (1971)), 337-340 · Zbl 0217.45503
[11] McIntosh, A., On the comparability of \(A^{12} and A^{∗12}\), (Proc. Amer. Math. Soc., 32 (1972)), 430-434 · Zbl 0248.47020
[12] Nirenberg, L.; Treves, F., On local solvability of linear partial differential equations, II, Comm. Pure Appl. Math., 23, 459-510 (1970) · Zbl 0208.35902
[13] Powers, R. T., A remark on the domain of an unbounded derivation of a \(C^∗\)-algebra, J. Functional Analysis, 18, 85-95 (1975) · Zbl 0299.46059
[14] Boas, R. P., Integrability Theorems for Trigonometric Transforms (1967), Springer-Verlag: Springer-Verlag Berlin · Zbl 0145.06804
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