Banach-Space Operators Acting on Semicircular Elements Induced by Orthogonal Projections

摘要

The main purposes of this paper are (i) to construct-and-study weighted-semicircular elements from mutually orthogonal vertical bar Z vertical bar-many projections, and the Banach *probability space L-Q generated by these operators, (ii) to establish *-isomorphisms on L-Q induced by shifting processes on the set Z of integers, (iii) to consider how the *-isomorphisms of (ii) generates Banach-space adjointable operators acting on the Banach *-algebra L-Q, (iv) to investigate operator-theoretic properties of the operators of (iii), and (v) to study how the Banach-space operators of (iii) distorts the original free-distributional data on L-Q. As application, one can check how the semicircular law is distorted by our Banach-space operators on L-Q.