Extensions of the representation theorems of Riesz and Fréchet
Mathematica Bohemica (1993)
- Volume: 118, Issue: 3, page 297-312
- ISSN: 0862-7959
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topPrandini, João C.. "Extensions of the representation theorems of Riesz and Fréchet." Mathematica Bohemica 118.3 (1993): 297-312. <http://eudml.org/doc/29078>.
@article{Prandini1993,
abstract = {We present two types of representation theorems: one for linear continuous operators on space of Banach valued regulated functions of several real variables and the other for bilinear continuous operators on cartesian products of spaces of regulated functions of a real variable taking values on Banach spaces. We use generalizations of the notions of functions of bounded variation in the sense of Vitali and Fréchet and the Riemann-Stieltjes-Dushnik or interior integral. A few applications using geometry of Banach spaces are given.},
author = {Prandini, João C.},
journal = {Mathematica Bohemica},
keywords = {Riesz type representation theorem; Fréchet type representation theorem; representation theorems; linear continuous operators on spaces of Banach valued regulated functions of several real variables; bilinear continuous operators on cartesian products; functions of bounded variation; interior integral; geometry of Banach spaces; spaces of regulated functions of a real variable taking values in Banach spaces; regulated functions; Riesz type representation theorem; Fréchet type representation theorem; representation theorems; linear continuous operators on spaces of Banach valued regulated functions of several real variables; bilinear continuous operators on cartesian products; functions of bounded variation; interior integral; geometry of Banach spaces; spaces of regulated functions of a real variable taking values in Banach spaces},
language = {eng},
number = {3},
pages = {297-312},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extensions of the representation theorems of Riesz and Fréchet},
url = {http://eudml.org/doc/29078},
volume = {118},
year = {1993},
}
TY - JOUR
AU - Prandini, João C.
TI - Extensions of the representation theorems of Riesz and Fréchet
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 3
SP - 297
EP - 312
AB - We present two types of representation theorems: one for linear continuous operators on space of Banach valued regulated functions of several real variables and the other for bilinear continuous operators on cartesian products of spaces of regulated functions of a real variable taking values on Banach spaces. We use generalizations of the notions of functions of bounded variation in the sense of Vitali and Fréchet and the Riemann-Stieltjes-Dushnik or interior integral. A few applications using geometry of Banach spaces are given.
LA - eng
KW - Riesz type representation theorem; Fréchet type representation theorem; representation theorems; linear continuous operators on spaces of Banach valued regulated functions of several real variables; bilinear continuous operators on cartesian products; functions of bounded variation; interior integral; geometry of Banach spaces; spaces of regulated functions of a real variable taking values in Banach spaces; regulated functions; Riesz type representation theorem; Fréchet type representation theorem; representation theorems; linear continuous operators on spaces of Banach valued regulated functions of several real variables; bilinear continuous operators on cartesian products; functions of bounded variation; interior integral; geometry of Banach spaces; spaces of regulated functions of a real variable taking values in Banach spaces
UR - http://eudml.org/doc/29078
ER -
References
top- C. S. Hönig, Volteгra-Stieltjes Integral Equations, Mathematical Studies 16, North Holland Pub. Comp., Amsterdam, 1975. (1975)
- M. Morse, W. Transue, A Calculus for Fréchet Variations, Journal of Indian Math. Soc. XIV (1950), 65-117. (1950) Zbl0040.05801MR0039043
- M. Morse, W. Transue, 10.4153/CJM-1950-033-1, Canadian Journal of Math. 2 (1950), 344-374. (1950) MR0037340DOI10.4153/CJM-1950-033-1
- G. C. Rocha-Filho, Integral de Riemann Vetorial e Geometria dos Espaços de Banach, doctoral thesis, IME-USP, 1979. (1979)
- J. A. Clarkson, C. R. Adams, 10.1090/S0002-9947-1933-1501718-2, Trans. Am. Math. Soc. 35 (1933), 824-854. (1933) MR1501718DOI10.1090/S0002-9947-1933-1501718-2
- M. Fréchet, 10.2307/1988990, Trans. Amer. Math. Soc. (1915), 215-234. (1915) MR1501010DOI10.2307/1988990
- N. Dunford, J. T. Schwartz, Linear Operators, paгt I, p. 337, Interscience, 1967. (1967)
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