×

Averaging and Reynolds operators on Banach algebras. I: Representation by derivations and antiderivations. (English) Zbl 0137.10202


PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Atkinson, F.V, Some aspects of Baxter’s functional equation, J. math. anal. appl., 7, 1-30, (1963) · Zbl 0118.12903
[2] Birkhoff, G, Moyenne des fonctions bornée, (), 149-153
[3] Dubreil-Jacotin, M.-L, Étude algébrique des transformations de Reynolds, (), 2-27 · Zbl 0088.32703
[4] Moy, S.-T.C, Characterizations of conditional expectation as a transformation of function spaces, Pacific J. math., 4, 47-63, (1954) · Zbl 0055.12503
[5] Rota, G.-C, On the representation of averaging operators, (), 52-64 · Zbl 0096.09101
[6] Rota, G.-C, Spectral theory of smoothing operators, (), 863-868 · Zbl 0099.09901
[7] Brainerd, B, On the structure of averaging operators, J. math. anal. appl., 5, 347-377, (1962) · Zbl 0116.32102
[8] Brainerd, B, Averaging operators on the ring of continuous functions on a compact space, J. Australian math. soc., 4, 293-298, (1964) · Zbl 0139.08404
[9] Kelley, J.L, Averaging operators on C∞(X), Illinois J. math., 2, 214-223, (1958) · Zbl 0080.32001
[10] Rota, G.-C, Reynolds operators, (), 70-83
[11] Birkhoff, G, Lattices in applied mathematics, II averaging operators, (), 163-184
[12] Miller, J.B, Möbius transforms of Reynolds operators, J. reine angew. math., 218, 6-16, (1965) · Zbl 0138.38302
[13] Hille, R; Phillips, R.S, Functional analysis and semi-groups, (), Providence
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.