Albrecht Pietsch Livres

Focusing on the advancements in the theory of nuclear locally convex spaces, this book discusses significant developments since the first edition, including the Universality Theorem by T. and Y. Komura, which confirms Grothendieck's conjecture. It highlights new existence theorems for bases and explores various classes of operators relevant to nuclear spaces. While most chapters remain largely unchanged, the tenth chapter has been substantially revised, and an independent eleventh chapter on universal nuclear locally convex spaces is introduced, along with a brief discussion on s-nuclear spaces.

Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.