ON MAPS THAT PRESERVE-PRODUCTS OF OPERATORS IN B(H)

Let B(H) be the C(*)-algebra of all bounded linear operators on Hilbert space H. In this paper, we introduce three concept of (*)-products on B(H), and present a form for a unital surjective bounded linear map [phi]: B(H) [right arrow] B(H), which preserves these (*)-products in both directions. Key words and phrases. Hilbert space; (*)-product; preserving linear map; C(*)-algebra.
1. INTRODUCTION AND PRELIMINARIES Suppose that X and Y are linear spaces and [phi]: X [right arrow] Y is a map. We say that [phi] is a preserving map in [...]