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This paper studies trace class perturbation of closed linear relations inHilbert spaces. The concept of trace class perturbation of closed relations isintroduced by orthogonal projections. Equivalent characterizations of compactand trace class block operator matrices are first given in terms of theirelements, separately. By using them, several equivalent and sufficientcharacterizations of trace class perturbation of closed linear relations areobtained.

Trace class perturbation of closed linear relations