Abstract
A typical result of this paper is the following: A closed linear operator T between Banach spaces X and Y is lower semi-Fredholm iff it is a rk-(=relatively compact)surjection, i.e. for every bounded sequence (yn) in Y there is a bounded sequence (xn) in D(T) such that (yn−Txn) is relatively compact in Y. The concept of co-(rk- and wk-)injections and surjections are introduced to characterize semi-Fredholm properties (in the usual or generalized sense). This is done also by new operator moduli.
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