General construction of Banach-Grassmann algebras

Vladimir G. Pestov

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1992)

  • Volume: 3, Issue: 3, page 223-231
  • ISSN: 1120-6330

Abstract

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We show that a free graded commutative Banach algebra over a (purely odd) Banach space E is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if E is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.

How to cite

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Pestov, Vladimir G.. "General construction of Banach-Grassmann algebras." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 3.3 (1992): 223-231. <http://eudml.org/doc/244069>.

@article{Pestov1992,
abstract = {We show that a free graded commutative Banach algebra over a (purely odd) Banach space \( E \) is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if \( E \) is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.},
author = {Pestov, Vladimir G.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Banach-Grassmann Algebras; Super analysis; Graded algebras; superanalysis; graded-commutative algebra; Banach-Grassmann algebra; superfield expansion; Jadczyk-Pilch self-duality property; Rogers algebra; exterior algebras over Banach spaces; free graded commutative Banach algebra over a Banach space},
language = {eng},
month = {9},
number = {3},
pages = {223-231},
publisher = {Accademia Nazionale dei Lincei},
title = {General construction of Banach-Grassmann algebras},
url = {http://eudml.org/doc/244069},
volume = {3},
year = {1992},
}

TY - JOUR
AU - Pestov, Vladimir G.
TI - General construction of Banach-Grassmann algebras
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1992/9//
PB - Accademia Nazionale dei Lincei
VL - 3
IS - 3
SP - 223
EP - 231
AB - We show that a free graded commutative Banach algebra over a (purely odd) Banach space \( E \) is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if \( E \) is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.
LA - eng
KW - Banach-Grassmann Algebras; Super analysis; Graded algebras; superanalysis; graded-commutative algebra; Banach-Grassmann algebra; superfield expansion; Jadczyk-Pilch self-duality property; Rogers algebra; exterior algebras over Banach spaces; free graded commutative Banach algebra over a Banach space
UR - http://eudml.org/doc/244069
ER -

References

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