k-拟-A类算子是次标量算子

k-quasi-class A operators are subscalar operators

本文证明了A类算子和与其可交换的k阶代数算子的和是12k+2阶次标量算子,并证明了每个k-拟-A类算子有一个标量扩张.作为推论,得到若此类算子的谱集有非空内点,则其有非平凡的不变子空间.最后研究了k-拟-A类算子的超不变子空间问题.

In this paper, we show that the sum of a class A operator and an algebraic operator of order k which are commuting is subscalar of order 12k＋2, we also prove that every k-quasi-class A operator has a scalar extension. As a consequence, we get that if the spectrum of such an operator has nonempty interior in C, then it has a nontrivial invariant subspace. We also examine the hyperinvariant subspace problem for k-quasi-class A operator.