×

Isometric operators in vector-valued \(L^ p\)-spaces. (English) Zbl 0612.46030

Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 107, 198-203 (Russian) (1982; Zbl 0515.46030).

MSC:

46E40 Spaces of vector- and operator-valued functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47B38 Linear operators on function spaces (general)

Citations:

Zbl 0515.46030
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] M. Cambern, ”The isometries of LP(X; K),” Pac. J. Math.,55, No. 1, 9–17 (1974). · Zbl 0277.46027 · doi:10.2140/pjm.1974.55.9
[2] A. R. Sourour, ”On the isometries of LP({\(\Omega\)}; X),” Bull. Am. Math. Soc.,83, No. 1, 129–130 (1977). · Zbl 0352.46025 · doi:10.1090/S0002-9904-1977-14213-4
[3] A. I. Plotkin, ”The continuation of LP-isometries,” J. Sov. Math.,2, No. 2 (1974). · Zbl 0283.46018
[4] A. I. Plotkin, ”An algebra that is generated by translation operators, and LP-norms,” Funkts. Analiz., Ul’yanovsk, No. 6, 112–121 (1976).
[5] W. Rudin, ”LP-isometries and equimeasurability,” Indiana Univ. Math. J.,25, No. 3, 215–228 (1976). · Zbl 0326.46011 · doi:10.1512/iumj.1976.25.25018
[6] A. L. Koldobskii, ”The continuation of isometries in Orlicz spaces,” in: Gertsenovskie Chteniya, Matematika, Leningrad (1977), pp. 61–66.
[7] A. L. Koldobskii, ”On isometric operators in LP(X; \(\mathbb{R}\)n),” Funkts. Analiz., Ul’yanovsk, No. 12, 90–99 (1979).
[8] J. Hoff man-J{\(\phi\)}rgensen, ”Measures which agree on balls,” Math. Scand.,37, No. 2, 319–326 (1975). · Zbl 0329.28002 · doi:10.7146/math.scand.a-11610
[9] N. I. Akhiezer, The Classical Moment Problems and Some Related Questions in Analysis, Oliver and Boyd, Edinburgh (1965). · Zbl 0135.33803
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.