On well-bounded operators

J. R. Ringrose

doi:10.1017/S1446788700026008

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This note is concerned with a question arising from some work of D. R. Smart (2). In the introduction we indicate the nature of the problem. Notations will be explained only in as far as they differ from those of (2).

References

[1]Hille, E., Functional Analysis and Semi-groups. Amer. Math. Soc. Colloquium Publications, 1948.Google Scholar

[2]Smart, D. R., Conditionally Convergent Spectral Expansions. This journal page 319.CrossRef Google Scholar

[3]Zaanen, A. C., Linear Analysis. North Holland Publish. Comp., Amsterdam, 1953.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Spain, P. G. 1972. On well-bounded operators of type (B). Proceedings of the Edinburgh Mathematical Society, Vol. 18, Issue. 1, p. 35.

Nikol'skii, N. K. 1976. Invariant subspaces in the theory of operators and theory of functions. Journal of Soviet Mathematics, Vol. 5, Issue. 2, p. 129.

Gillespie, T. A. 1976. Commuting well-bounded operators on Hilbert spaces. Proceedings of the Edinburgh Mathematical Society, Vol. 20, Issue. 2, p. 167.

Fong, C. K. and Lam, Louisa 1981. On spectral theory and convexity. Transactions of the American Mathematical Society, Vol. 264, Issue. 1, p. 59.

Jibril, Adnan A. S. 1983. On well-bounded operators of class Г. Glasgow Mathematical Journal, Vol. 24, Issue. 1, p. 1.

Ricker, Werner 1987. Well-bounded operators of type (B) in a class of Banach spaces. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 42, Issue. 3, p. 399.

Berkson, Earl and Gillespie, T.A 1987. Stečkin's Theorem, transference, and spectral decompositions. Journal of Functional Analysis, Vol. 70, Issue. 1, p. 140.

Kluvánek, Igor 1988. Scalar operators and integration. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 45, Issue. 3, p. 401.

Doust, Ian and Bozhou, Qiu 1993. The spectral theorem for well-bounded operators. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 54, Issue. 3, p. 334.

Doust, Ian 1994. A weaker condition for normality. Glasgow Mathematical Journal, Vol. 36, Issue. 2, p. 249.

Karayannakis, Dimitri Lambrou, Michael S. and Magiropoulos, Manolis 1997. Spectral Decompositions of Isometries oncp. Journal of Mathematical Analysis and Applications, Vol. 215, Issue. 1, p. 190.

Doust, Ian and Terauds, Venta 2010. Extensions of an AC(σ) functional calculus. Journal of Mathematical Analysis and Applications, Vol. 362, Issue. 1, p. 100.

Doust, Ian Leinert, Michael and Stoneham, Alan 2023. The Banach Algebras $$AC(\sigma )$$ and $$BV(\sigma )$$. Results in Mathematics, Vol. 78, Issue. 1,

Doust, Ian Leinert, Michael and Stoneham, Alan 2023. Approximation in $$AC(\sigma )$$. Banach Journal of Mathematical Analysis, Vol. 17, Issue. 1,

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On well-bounded operators

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