On the structure of principal ideals of operators

Authors:
G. D. Allen and L. C. Shen

Journal:
Trans. Amer. Math. Soc. **238** (1978), 253-270

MSC:
Primary 47B05; Secondary 47D99

MathSciNet review:
0467371

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Abstract: This paper considers various types of principal ideals generated by single compact operators on a separable Hilbert space. In particular, necessary and sufficient condtions that a principal ideal be normable are given. Relations between principal ideals and duals of Lorentz and Orlicz spaces are also given. All conditions are expressed using the singular numbers of the operator.

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DOI:
https://doi.org/10.1090/S0002-9947-1978-0467371-4

Article copyright:
© Copyright 1978
American Mathematical Society