Annals of Functional Analysis

On the equivalence of some concepts in the theory of Banach algebras

Józef Banaś and Leszek Olszowy

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


Our principal aim in this article is to show the equivalence of two concepts used recently in the theory of Banach algebras. The result we present here solves an open problem raised by Jeribi and Krichen in their 2015 book.

Article information

Ann. Funct. Anal., Volume 10, Number 2 (2019), 277-283.

Received: 26 July 2018
Accepted: 11 October 2018
First available in Project Euclid: 22 March 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Secondary: 46H99: None of the above, but in this section

Banach algebra weak convergence weak compactness WC-Banach algebra condition $(\mathcal{P})$


Banaś, Józef; Olszowy, Leszek. On the equivalence of some concepts in the theory of Banach algebras. Ann. Funct. Anal. 10 (2019), no. 2, 277--283. doi:10.1215/20088752-2018-0027.

Export citation


  • [1] J. Appell, J. Banaś, and N. Merentes, Bounded Variation and Around, De Gruyter Ser. Nonlinear Anal. Appl. 17, De Gruyter, Berlin, 2014.
  • [2] J. Banaś and M.-A. Taoudi, Fixed points and solutions of operator equations for the weak topology in Banach algebras, Taiwanese J. Math. 18 (2014), no. 3, 871–893.
  • [3] A. Ben Amar, M. Boumaiza, and D. O’Regan, Hybrid fixed point theorems for multivalued mappings in Banach algebras under a weak topology setting, Fixed Point Theory Appl. 18 (2016), no. 2, 327–350.
  • [4] A. Ben Amar, S. Chouayekh, and A. Jeribi, New fixed point theorems in Banach algebras under weak topology features and applications to nonlinear integral equations, J. Funct. Anal. 259 (2010), no. 9, 2215–2237.
  • [5] A. Ben Amar, S. Chouayekh, and A. Jeribi, Fixed point theory in a new class of Banach algebras and applications, Afr. Mat. 24 (2013), no. 4, 705–724.
  • [6] N. Dunford and J. T. Schwartz, Linear Operators, I, reprint of the 1959 original, Wiley Classics Lib., Wiley, New York, 1988.
  • [7] J. Garcia-Falset and K. Latrach, Krasnoselskii-type fixed point theorems for weakly sequentially continuous mappings, Bull. Lond. Math. Soc. 44 (2012), no. 1, 25–38.
  • [8] A. Jeribi and B. Krichen, Nonlinear Functional Analysis in Banach Spaces and Banach Algebras: Fixed Point Theory Under Weak Topology for Nonlinear Operators and Block Operator Matrices with Applications, Monogr. Res. Notes Math., CRC Press, Boca Raton, 2016.
  • [9] A. Jeribi, B. Krichen, and B. Mefteh, Fixed point theory in WC-Banach algebras, Turkish J. Math. 40 (2016), no. 2, 283–291.
  • [10] B. Mefteh, Fixed point theorems in WC-Banach algebras and applications, preprint, 2018.
  • [11] W. Rudin, Real and Complex Analysis, 3rd ed., McGraw-Hill, New York, 1987.