Essentially subnormal operators
Essentially subnormal operators
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DOI：
10.1090/s0002-9939-99-05053-4
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
N. Feldman
中科院分区：
文献类型：
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作者：
N. Feldman
一个算子本质上是次正规的，如果它在Calkin代数中的像是次正规的。我们将本质次正规算子刻画为具有本质正规扩张的算子。事实上，它表明，本质次正规算子有一个扩展的形式“正常加紧”。定义了本质正规谱，并利用它刻画了本质等距性。证明了每一个本质次正规算子都可以分解为一个次正规算子与一些不可约本质次正规算子的直和。Putnam不等式的一个基本版本被证明为这些运营商。此外，还证明了本质正规性是本质次正规算子类中的相似不变量。对本质亚正规算子类也作了简要的讨论，并给出了几个本质亚正规算子的例子。
An operator is essentially subnormal if its image in the Calkin algebra is subnormal. We shall characterize the essentially subnormal operators as those operators with an essentially normal extension. In fact, it is shown that an essentially subnormal operator has an extension of the form “Normal plus Compact”. The essential normal spectrum is defined and is used to characterize the essential isometries. It is shown that every essentially subnormal operator may be decomposed as the direct sum of a subnormal operator and some irreducible essentially subnormal operators. An essential version of Putnam’s Inequality is proven for these operators. Also, it is shown that essential normality is a similarity invariant within the class of essentially subnormal operators. The class of essentially hyponormal operators is also briefly discussed and several examples of essentially subnormal operators are given.