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In Spectral Properties of Certain Operators on a Free Hilbert Space and the Semicircular Law, the authors consider the so-called free Hilbert spaces, which are the Hilbert spaces… Read more
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1. Fundamentals
1.1. Introduction
1.2. Free Probability
1.3. Semicircular Elements
2. Semicircular Elements Induced by Orthogonal Projections
2.1. The Banach *-Algebra Induced by Orthogonal Projections
2.2. Weighted-Semicircular Elements Induced by Q
2.3. Semicircular Elements Induced by Q
3. Semicircular Elements Induced by Projections On l2-Spaces
3.1. The Cloned C*-Algebra of B (l2 (N0))
3.2. Semicircular Elements Induced by Q
3.3. Semicircular Elements Induced by A x B (l2 (N0))
3.4. Applications
4. Jump Operators on Free Hilbert Spaces and Deformed Semicircular Laws
4.1. Hilbert Spaces F [H1, ..., HN]
4.2. Jump Operators on F [H1, ..., HN]
4.3. Semicircular Elements Induced by F [H1, ..., HN]
4.4. Jump Operators of B (F) and Semicircularity on LQ [H1, ..., HN]
4.5. The Semicircular Law on LQ [H1, ..., HN]
5. Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws
5.1. Shift Operators on F [H1, ..., HN]
5.2. Shift Operators on F and Semicircularity on LQ [H1, ..., HN]
5.3. Shift Operators of B (F) Acting on LQ [H1, ..., HN]
6. Jump-Shift Operators on Free Hilbert Spaces and Deformed Semicircular Laws
6.1. Jump-Shift Operators on F [H1, ..., HN]
6.2. Jump-Shift Operators on F and Semicircularity on LQ [H1, ..., HN]
IC
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