An intersection theorem in Banach spaces

Alfonso Vignoli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1970)

  • Volume: 49, Issue: 3-4, page 180-183
  • ISSN: 0392-7881

Abstract

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Let the Banach space X = A ⊕ B be the direct sum of two subspaces A , B ⊂ X , and let f : A → X , g : B → X be continuous mappings. A condition is given on f and g in order to ensure that the intersection f ⁢ ( A ) ∩ g ⁢ ( B ) is not empty.

How to cite

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Vignoli, Alfonso. "An intersection theorem in Banach spaces." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 49.3-4 (1970): 180-183. <http://eudml.org/doc/296032>.

@article{Vignoli1970,
abstract = {Let the Banach space $X = A \oplus B$ be the direct sum of two subspaces $A, B \subset X$, and let $f : A \to X$, $g : B \to X$ be continuous mappings. A condition is given on $f$ and $g$ in order to ensure that the intersection $f(A) \cap g(B)$ is not empty.},
author = {Vignoli, Alfonso},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
language = {eng},
month = {9},
number = {3-4},
pages = {180-183},
publisher = {Accademia Nazionale dei Lincei},
title = {An intersection theorem in Banach spaces},
url = {http://eudml.org/doc/296032},
volume = {49},
year = {1970},
}

TY - JOUR
AU - Vignoli, Alfonso
TI - An intersection theorem in Banach spaces
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1970/9//
PB - Accademia Nazionale dei Lincei
VL - 49
IS - 3-4
SP - 180
EP - 183
AB - Let the Banach space $X = A \oplus B$ be the direct sum of two subspaces $A, B \subset X$, and let $f : A \to X$, $g : B \to X$ be continuous mappings. A condition is given on $f$ and $g$ in order to ensure that the intersection $f(A) \cap g(B)$ is not empty.
LA - eng
UR - http://eudml.org/doc/296032
ER -

References

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  1. GRANAS, A., On a geometrical theorem in Banach spaces, «Bull. Acad. Pol. Sci. Cl. III», 5, N.9, 873-877 (in Russian), (1957). Zbl0078.11702MR91433
  2. KURATOWSKI, C., Topologie, «Monografie Matematiczne», Tom 20, Warszawa1958. 
  3. DARBO, G., Punti uniti in trasformazioni a codominio non compatto, «Rend. Sem. Mat. Padova», 24, 84-92 (1955). Zbl0064.35704MR70164
  4. FURI, M. and VIGNOLI, A., A fixed point theorem in complete metric spaces, «Boll. Un. Mat. It.», serie IV, N. 4-5, 505-509 (1969). Zbl0183.51404MR256378
  5. GRANAS, A., On a class of nonlinear mappings in Banach spaces, «Bull. Acad. Pol. Sci. Cl. III», 5, N.9, 867-870 (1957). Zbl0078.11701MR91432
  6. VIGNOLI, A., On quasibounded mappings and nonlinear functional equations (to appear). Zbl0254.47089MR303379
  7. PETRYSHYN, W. V., Further remarks on nonlinear P-compact operators in Banach space, «J. Math. Anal. Appl.», 16, N.2, 243-253 (1966). Zbl0149.10603MR198299DOI10.1016/0022-247X(66)90169-7

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