C余弦算子函数的对偶及其次生成元的性质
The Adjoint of a C-cosine Operator Function and Its Subgenerators
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摘要: 讨论了C-余弦算子函数的对偶及其次生成元的性质.证明了C-余弦算子函数的每个次生成元的对偶必是其对偶余弦算子函数的次生成元；反之，对对偶余弦算子函数的每个次生成元S必有原余弦算子函数的某个次生成元B，使得B*是S的弱*闭包.并对最大元、最小元作了对应比较.Abstract: We discuss the relationship between the subgenerators of a C-cosine operator functio n and its adjoint. We prove that every subgenerator of a C-cosine operator function is the subgenerator of its adjoint, and, conversely, for every subgener ator S of the adjoint cosine operator function, there exists a subgenerator B* is the weak*-closure of S. We also compare the smallest and larg est elements of the C-cosine operator function with those of the adjoint ac cordingly.
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Key words:
- semigroup of operators /
- C-cosine operator func tion /
- subgenerator /
- adjoint. .
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