Covered topics include Banach and Hilbert spaces, Hahn-Banach theorem, dual spaces, orthonormal bases, measure spaces, Lebesgue integration, convergence theorems, Lp-spaces and their duals, ...

Topics covered are: an introduction to locally convex spaces (including the Hahn-Banach separation theorem, weak and weak*-topologies, Alaoglu´s theorem, Krein-Milman´s theorem); more on operators on ...

Representability of Polish groups on reflexive Banach spaces Francesca Zhehan Yu Advisor ... Another important milestone is the 1989 theorem of Martin and Steel that, if there are infinitely many ...

In 2022, two high school students created a trigonometric proof of the Pythagorean Theorem—something that’s only ever been accomplished by a few professional mathematicians. Now, a new article ...

PhD students and postdoctoral researchers: Students and postdoctoral researchers who are interested to join my research group at the Chinese University of Hong Kong, Shenzhen in China and at the ...

Sequences of real numbers, the notion of convergence of a sequence, completeness, the Bolzano-Weierstrass theorem, limits of series of non-negative reals and convergence tests. Analytical definition ...

The Pythagorean theorem remains fundamental in mathematics and is taught in schools across the world. The Greek philosopher and mathematician was born on Samos to an aristocratic family in 570 BC. He ...

This manuscript describes a potentially important theoretical framework to link predictive coding, error-based learning, and neuronal dynamics. The provided evidence is solid, but some details would ...