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Gleason's theorem and its applications
Autor: Dvurečenskij Anatolij
Rok: c1993.
ISBN: 9788090048614
ISBN: 9780792319900
OKCZID: 110109203
Citace (dle ČSN ISO 690):
DVUREČENSKIJ, Anatolij. Gleason's theorem and its applications. Bratislava: Ister Science Press, c1993. xv, 325 s.
Anotace
This volume deals with Gleason's theorem and Gleason's measures and indicates the many ways in which they can be applied. The book comprises five chapters. Chapter 1 is devoted to elements of Hilbert space theory. Chapter 2 is devoted to quantum logic theory. Gleason's theorem is described and proved in Chapter 3, together with proofs for measures that can attain infinite values. In Chapter 4 the possibility of applying Gleason's theorem to the completeness criteria of inner product spaces is addressed. Chapter 5 discusses orthogonal measures and the unexpected possibility of describing states on Keller spaces, as well as other applications. Throughout the book, important facts and concepts are illustrated exercises. For mathematicians and physicists interested in the mathematical foundations of quantum mechanics, and those whose work involves noncommutative measure theory, orthomodular lattices. Hilbert space theory and probability theory.