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The Mathematical Research of Juan Carlos Ferrando

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Functional Analysis and Continuous Optimization (IMFACO 2022)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 424))

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Abstract

This chapter is based on my invited talk at the International Meeting on Functional Analysis and Continuous Optimization dedicated to Juan Carlos Ferrando at the occasion of his 65 birthday at University Miguel Hernández in Elche, Spain, on June 16–17, 2022. We examine several topics of the research work of Professor Juan Carlos Ferrando. After the introductory section, this chapter is divided into seven sections, which include his research on Topological Vector Spaces, on Nikodým boundedness theorem, on distinguished Fréchet spaces, on \(C_{p}\)-theory, on \(C_{k}\)-theory, on the weak topology of \(C_{k}(X)\) and on the bidual of \(C_{p}(X)\). The section Research on Topological Vector Spaces contains four subsections. The proofs of Professor Ferrando are very clear and elegant. We have included several proofs, mainly in the sections devoted to \(C_{p}\)-theory and \(C_{k}\)-theory, developed in the last five years.

Dedicated to Juan Carlos Ferrando on the occasion of his 65th birthday.

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Acknowledgements

My gratitude to Miguel Hernández University and in particular to CIO Institute and to Department of Statistics, Mathematics and Informatics by the organization and support of the International Meeting on Functional Analysis and Continuous Optimization dedicated to Juan Carlos Ferrando on the occasion of his 65 birthday in Elche, Spain, on June 16-17, 2022. I have been very honored by the invitation to participate in this Meeting with a talk on the research work of professor Juan Carlos Ferrando.

I also thank the work of professors María Josefa Cánovas Cánovas, José María Amigó García and Marco Antonio López-Cerdá who have organized, developed and managed this International Meeting with my congratulations by this wonderful Meeting.

And finally, last but not least, my gratitude to professor Juan Carlos Ferrando by his friendship for almost 40 years, my respect for his enormous work capacity, and my admiration for his amazing sharpness and ability in research. Juan Carlos is a stimulating example for all of us who have known him. I would like to continue working in mathematics with my excellent and admired friend Juan Carlos Ferrando for many more years.

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  1. IUMPA, Professor Emeritus at Universitat Politècnica de València, 46022, Valencia, Spain

    Manuel López-Pellicer

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  1. Manuel López-Pellicer
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Correspondence to Manuel López-Pellicer .

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  1. Center of Operations Research, Miguel Hernández University of Elche, Elche, Alicante, Spain

    José M. Amigó

  2. Center of Operations Research, Miguel Hernández University of Elche, Elche, Alicante, Spain

    María J. Cánovas

  3. Department of Mathematics, Alicante University, San Vicente del Raspeig, Alicante, Spain

    Marco A. López-Cerdá

  4. Institute for Pure and Applied Mathematics (IUMPA), Polytechnic University of Valencia, Valencia, Spain

    Manuel López-Pellicer

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López-Pellicer, M. (2023). The Mathematical Research of Juan Carlos Ferrando. In: Amigó, J.M., Cánovas, M.J., López-Cerdá, M.A., López-Pellicer, M. (eds) Functional Analysis and Continuous Optimization. IMFACO 2022. Springer Proceedings in Mathematics & Statistics, vol 424. Springer, Cham. https://doi.org/10.1007/978-3-031-30014-1_1

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