Pointwise induced operators on $L_{p}$-spaces
HTML articles powered by AMS MathViewer
- by Anzelm Iwanik PDF
- Proc. Amer. Math. Soc. 58 (1976), 173-178 Request permission
Abstract:
In this note we present a characterization of pointwise induced operators on ${L_p}$-spaces with finite measures, $1 \leq p < \infty$. An operator $P$ is pointwise induced if and only if $|Pu| = P|u|$ and $P1 = 1$. As an application we obtain a characterization of the linear positive isometries mapping 1 into 1.References
-
S. Banach, Théorie des opérations linéaires, Monografie Mat., PWN, Warsaw, 1932; reprint, Chelsea, New York, 1955. MR 17, 175.
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- A. J. Ellis, Extreme positive operators, Quart. J. Math. Oxford Ser. (2) 15 (1964), 342–344. MR 173950, DOI 10.1093/qmath/15.1.342
- M. Solveig Espelie, Multiplicative and extreme positive operators, Pacific J. Math. 48 (1973), 57–66. MR 336438
- John Lamperti, On the isometries of certain function-spaces, Pacific J. Math. 8 (1958), 459–466. MR 105017
- G. Lumer, Isometries of Orlicz spaces, Bull. Amer. Math. Soc. 68 (1962), 28–30. MR 131764, DOI 10.1090/S0002-9904-1962-10686-7
- Gunter Lumer, On the isometries of reflexive Orlicz spaces, Ann. Inst. Fourier (Grenoble) 13 (1963), 99–109. MR 158259
- R. R. Phelps, Extreme positive operators and homomorphisms, Trans. Amer. Math. Soc. 108 (1963), 265–274. MR 156224, DOI 10.1090/S0002-9947-1963-0156224-6
- Roman Sikorski, On the inducing of homomorphisms by mappings, Fund. Math. 36 (1949), 7–22. MR 31535, DOI 10.4064/fm-36-1-7-22
- Roman Sikorski, Boolean algebras, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 25, Academic Press, Inc., New York; Springer-Verlag, Berlin-New York, 1964. MR 0177920
- Kôsaku Yosida, Functional analysis, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 123, Springer-Verlag New York, Inc., New York, 1968. MR 0239384
- Helmut H. Schaefer, Banach lattices and positive operators, Die Grundlehren der mathematischen Wissenschaften, Band 215, Springer-Verlag, New York-Heidelberg, 1974. MR 0423039
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 173-178
- MSC: Primary 47B37; Secondary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-1976-0412883-6
- MathSciNet review: 0412883