Seminar on Operator Theory
主講者: 曹鵬教授(北京理工大學)
講題: Scattering Elements in the Banach Algebra
時間: 2012-09-19 (Wed.)  10:30 - 12:00
地點: 數學所 617 研討室 (台大院區)
Abstract: It is well known that in a Banach algebra, if the set of quasinilpotent elements is a linear subspace, or a semigroup, then this set equals the Jacobson Radicals. In this talk, we will consisder the similar case for the elements with at most countable spectrum, which are called scattered elements. Firstly, we will give the definition of scattered radical, and show that the scattered radical has many properties as the Jacobson Radical. Then we will give some equilavent conditions: (i) $S(A)+S(A)\subset S(A);$ (ii) $S(A)S(A)\subset S(A);$ (iii) $[S(A),A]\subset R_{sc}(A).$ where, $S(A)$ means the set of scattered elements in the Banach algebras $A$ , and $R_{sc}(A)$ means the scattered radical of $A$.
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