ISOMORPHIC THEOREM BETWEEN ALGEBRA GENERATED BY IDEMPOTENTS AND ALGEBRA OF THEIR SYMBOLS

抄録

In this paper we constructed separately the algebras generated by the idempotents operators, and by nilpotents operators, and prove the isomorphic theorems between original algebras and algebras of symbols. In particular, Theorems 2.1, 2.2 prove that an operator is generalized invertible if and only if so its symbol is.