Ordered Structures of Constructing Operators for Generalized Riesz Systems
2018 ◽
Vol 2018
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pp. 1-8
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Keyword(s):
A sequence {φn} in a Hilbert space H with inner product <·,·> is called a generalized Riesz system if there exist an ONB e={en} in H and a densely defined closed operator T in H with densely defined inverse such that {en}⊂D(T)∩D((T-1)⁎) and Ten=φn, n=0,1,⋯, and (e,T) is called a constructing pair for {φn} and T is called a constructing operator for {φn}. The main purpose of this paper is to investigate under what conditions the ordered set Cφ of all constructing operators for a generalized Riesz system {φn} has maximal elements, minimal elements, the largest element, and the smallest element in order to find constructing operators fitting to each of the physical applications.
1995 ◽
Vol 37
(2)
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pp. 173-178
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2004 ◽
Vol 07
(02)
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pp. 233-247
1965 ◽
Vol 17
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pp. 1030-1040
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1999 ◽
Vol 22
(1)
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pp. 97-108
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1962 ◽
Vol 14
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pp. 651-659
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Keyword(s):
1991 ◽
Vol 34
(1)
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pp. 23-30
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Keyword(s):
1987 ◽
Vol 30
(4)
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pp. 421-428
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