Published July 10, 2023 | Version v1
Publication Open

Pointwise coproximinality in \(L^p(\mu, X)\)

Creators

  • 1. Tafila Technical University

Description

Let \(X\) be a Banach space, \(G\) be a closed subspace of \(X\), \((\Omega,\Sigma,\mu)\) be a \(\sigma\)-finite measure space, \(L(\mu,X)\) be the space of all strongly measurable functions from \(\Omega\) to \(X\), and \(L^{p}(\mu,X)\) be the space of all Bochner \(p-\)integrable functions from \(\Omega\) to \(X\). Discussing the relationship between the pointwise coproximinality of \(L(\mu, G)\) in \(L(\mu, X)\) and the pointwise coproximinality of \(L^{p}(\mu, G)\) in \(L^{p}(\mu, X)\) is the purpose of this paper.

⚠️ This is an automatic machine translation with an accuracy of 90-95%

Translated Description (Arabic)

لنفترض أن \( X\) مساحة بنك، \( G\) تكون مساحة فرعية مغلقة من \( X\)، \((\ Omega,\Sigma,\ mu)\) تكون مساحة قياس \(\sigma\) محدودة، \( L (\ mu,X)\) تكون مساحة جميع الوظائف القابلة للقياس بقوة من \(\Omega\) إلى \( X\)، و \( L^{ p }(\mu,X)\) تكون مساحة جميع وظائف Bochner \( p -\) المتكاملة من \(\Omega\) إلى \( X\). إن الغرض من هذه الورقة هو مناقشة العلاقة بين التناظر المشترك النقطي لـ \( L (\mu, G)\) في \( L (\ mu, X)\) والتناظر المشترك النقطي لـ \( L^{ p }(\ mu, G)\) في \( L ^{ p }(\ mu, X)\).

Translated Description (French)

Soit \(X\) un espace de Banach, \(G\) un sous-espace fermé de \(X\), \(((\Omega,\Sigma,\mu)\) un espace de mesure\(\ sigma\) -fini, \(L(\mu,X)\) l'espace de toutes les fonctions fortement mesurables de \(\Omega\) à \(X\), et \(L^{p}(\mu,X)\) l'espace de toutes les fonctions intégrables de Bochner \(p-\) de \(\Omega\) à \(X\). Discuter de la relation entre la coproximinalité ponctuelle de \(L(\mu, G)\) dans \(L(\mu, X)\) et la coproximinalité ponctuelle de \(L^{p}(\mu, G)\) dans \(L^{p}(\mu, X)\) est le but de cet article.

Translated Description (Spanish)

Sea \(X\) un espacio de Banach, \(G\) un subespacio cerrado de \(X\), \((\Omega,\Sigma,\mu)\) un espacio de medida finito\(\ sigma\), \(L(\mu,X)\) el espacio de todas las funciones fuertemente medibles de \(\Omega\) a \(X\), y \(L^{p}(\mu,X)\) el espacio de todas las funciones integrables de Bochner \(p-\) de \(\Omega\) a \(X\). Discutir la relación entre la coproximinalidad puntual de \(L(\mu, G)\) en \(L(\mu, X)\) y la coproximinalidad puntual de \(L^{p}(\mu, G)\) en \(L^{p}(\mu, X)\) es el propósito de este artículo.

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Additional details

Additional titles

Translated title (Arabic)
التماثل النقطي في \( L^p(\mu, X)\)
Translated title (French)
Coproximinalité ponctuelle dans \(L^p(\mu, X)\)
Translated title (Spanish)
Coproximinalidad puntual en \(L^p(\mu, X)\)

Identifiers

Other
https://openalex.org/W4385402288
DOI
10.33993/jnaat521-1328

Is supplement to
https://openalex.org/W42113618 (Other)
https://openalex.org/W3197542402 (Other)
https://openalex.org/W2971527398 (Other)
https://openalex.org/W2645958880 (Other)
https://openalex.org/W2140020064 (Other)
https://openalex.org/W2103468410 (Other)
https://openalex.org/W1968809652 (Other)
https://openalex.org/W1856228368 (Other)
https://openalex.org/W143502885 (Other)
https://openalex.org/W1025150868 (Other)

GreSIS Basics Section

Is Global South Knowledge
Yes
Country
Jordan

References

  • https://openalex.org/W1970033187
  • https://openalex.org/W1975761024
  • https://openalex.org/W1988583482
  • https://openalex.org/W2058406771
  • https://openalex.org/W2073428118
  • https://openalex.org/W2977234919
  • https://openalex.org/W4241008512
  • https://openalex.org/W4285616845