Topics in Contemporary Mathematical Analysis and Applications

1 Certain Banach-Space Operators Acting on Free Poisson Elements Induced by Orthogonal Projections

Ilwoo Cho

Saint Ambrose University

CONTENTS

1.1     Introduction

1.2     Preliminaries

1.3     Some Banach *-Algebras Induced by Projections

1.4     Weighted-Semicircular Elements Induced by Q

1.5     Semicircular Elements Induced by Q

1.6     The Semicircular Filterization (𝕃_Q, τ)

1.7     Free Poisson Elements Of 𝕃_Q

1.7.1     Free Poisson Elements

1.7.2     Certain Free Poisson Elements Induced By 𝒮

1.7.3     Some Free Poisson Elements Induced By 𝒮 ∪ χ

1.8     Free Weighted-Poisson Elements Of 𝕃_Q

1.8.1     Free Weighted-Poisson Elements

1.8.2     Free Weighted-Poisson Elements Induced By 𝒮∪χ

1.8.3     Free Weighted-Poisson Elements Induced By ...