Complexifications of real Banach spaces, polynomials and multilinear maps

Gustavo Muñoz; Yannis Sarantopoulos; Andrew Tonge

Studia Mathematica (1999)

  • Volume: 134, Issue: 1, page 1-33
  • ISSN: 0039-3223

Abstract

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We give a unified treatment of procedures for complexifying real Banach spaces. These include several approaches used in the past. We obtain best possible results for comparison of the norms of real polynomials and multilinear mappings with the norms of their complex extensions. These estimates provide generalizations and show sharpness of previously obtained inequalities.

How to cite

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Muñoz, Gustavo, Sarantopoulos, Yannis, and Tonge, Andrew. "Complexifications of real Banach spaces, polynomials and multilinear maps." Studia Mathematica 134.1 (1999): 1-33. <http://eudml.org/doc/216620>.

@article{Muñoz1999,
abstract = {We give a unified treatment of procedures for complexifying real Banach spaces. These include several approaches used in the past. We obtain best possible results for comparison of the norms of real polynomials and multilinear mappings with the norms of their complex extensions. These estimates provide generalizations and show sharpness of previously obtained inequalities.},
author = {Muñoz, Gustavo, Sarantopoulos, Yannis, Tonge, Andrew},
journal = {Studia Mathematica},
keywords = {complexification of Banach space; polynomial in Banach space; Chebyshev polynomial},
language = {eng},
number = {1},
pages = {1-33},
title = {Complexifications of real Banach spaces, polynomials and multilinear maps},
url = {http://eudml.org/doc/216620},
volume = {134},
year = {1999},
}

TY - JOUR
AU - Muñoz, Gustavo
AU - Sarantopoulos, Yannis
AU - Tonge, Andrew
TI - Complexifications of real Banach spaces, polynomials and multilinear maps
JO - Studia Mathematica
PY - 1999
VL - 134
IS - 1
SP - 1
EP - 33
AB - We give a unified treatment of procedures for complexifying real Banach spaces. These include several approaches used in the past. We obtain best possible results for comparison of the norms of real polynomials and multilinear mappings with the norms of their complex extensions. These estimates provide generalizations and show sharpness of previously obtained inequalities.
LA - eng
KW - complexification of Banach space; polynomial in Banach space; Chebyshev polynomial
UR - http://eudml.org/doc/216620
ER -

References

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