Dichotomy between operators acting on finite and infinite dimensional Hilbert spaces

Document Type : Research Article


1 Departamento de Análisis Matem\ático, Facultad de Matemáticas, Instituto de Matemáticas Antonio de Castro Brzezicki, Universidad de Sevilla, Avenida Reina Mercedes, Sevilla, 41080, Spain.

2 Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran.

3 Instituto de Matemática Interdisciplinar (IMI), Departamento de Análisis Matemático y Matemática Aplicada, Facultad de Ciencias Matemáticas, Plaza de Ciencias 3, Universidad Complutense de Madrid, Madrid, 28040, Spain.


In this expository article, we give several examples showing how drastically different can be the behavior of operators acting on finite versus infinite dimensional Hilbert spaces. This essay is written as in such a friendly-reader to show that the situation in the infinite dimensional setting is trickier than the finite one.


Main Subjects

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