Carlos S. Kubrusly Libri

The textbook offers a classical approach to measure theory, structured in two parts. The first part introduces an abstract perspective on measure and integration, emphasizing the significance of Lebesgue measure and integral as specific instances of broader concepts. The second part caters to advanced readers, focusing on measure and integration within topological spaces, ideal for a subsequent graduate course. This thoughtful design ensures a comprehensive understanding of both foundational and advanced topics in measure theory.

This book explores the research surrounding Hilbert-space operators, focusing on the invariant subspace problem—whether every operator has a nontrivial invariant subspace. It discusses significant results and models in operator theory, highlighting the ongoing quest for understanding these operators over nine comprehensive chapters.

The book offers a comprehensive introduction to the spectral theory of Hilbert space operators, focusing on recent theoretical advancements. It includes detailed proofs and thoroughly covers various intricate aspects and often overlooked features of the subject, making it a valuable resource for those seeking a deeper understanding of spectral theory.

Focusing on bilinear maps and tensor products, this book guides readers from foundational concepts in functional analysis to advanced topics in tensor theory, particularly in infinite-dimensional normed spaces. It emphasizes bilinear maps as essential tools for developing a coherent understanding of tensor products. The author employs a clear and approachable style, ensuring that complex ideas are accessible. With introductory chapters on linear and normed spaces, it prepares readers for further exploration in the field, making it suitable for those with basic knowledge in functional analysis.