Spectral theory of linear operators and spectral systems in Banach algebras

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This book focuses on the spectral theory of linear operators in Banach spaces and elements in Banach algebras, offering a comprehensive survey of various spectra types, including one-sided spectra, approximate point, essential, local, and Taylor spectra, along with their variants. The theory is presented in a unified, axiomatic, and elementary manner, with many results appearing for the first time in a monograph. The content is self-contained, requiring only a basic understanding of functional analysis, topology, and complex analysis. The second edition introduces new findings, particularly regarding orbits and their connection to the invariant subspace problem. Its clear writing style and well-organized material make it suitable for both students eager to learn about spectral theory and experts seeking reference material. This book serves as an excellent introduction to the field while also providing valuable insights into specific spectral theory topics for practicing mathematicians.