In this paper the fine structure of the spectrum of a closed linear operator T is studied in terms of the ascent, descent, nullity and defect of the operators )~-T. Several characterizations of poles of the resolvent operator Ra(T) are obtained:and these are used to characterize certain classes of operators, e.g., the class of meromorphic operators. Much of the underlying algebraic theory was developed by A. E. Taylor [17] and M. A. Kaashoek [8]. Their notation will be used throughout this paper.
We present arguments to support the existence of weight spaces for supersymmetric field theories and identify the calculations of information about supermultiplets to define such spaces via the concept of “holoraumy.” For the first time, this is extended to the complex linear superfield by a calculation of the commutator of supercovariant derivatives on all of its component fields.
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