No abstract

In this paper we prove a structure theorem for the class of $\mathcal{AN}$-operators between separable, complex Hilbert spaces which is similar to that of the singular value decomposition of a compact operator. Apart from this, we show that a bounded operator is $\mathcal{AN}$ if and only if it is either compact or a sum of a compact operator and scalar multiple of an isometry satisfying some condition. We obtain characterizations of these operators as a consequence of this structure theorem and deduce several properties which are similar to those of compact operators.

SUMMARYThe paper presents a displacement incrementation procedure to handle multiple loadings in post-buckling analysis of structures by Dynamic Relaxation (DR). This procedure is generalized and a 'variable-arc-length' method is proposed to automate the tracing of loaddeflection path. The resulting algorithm exactly traces limit points and can handle 'snap-through or 'snap-back' problems. The efficiency of the proposed method is demonstrated by typical examples of truss, beam and shell structures.

No abstract

Let T : H 1 Ñ H 2 be a bounded linear operator defined between complex Hilbert spaces H 1 and H 2 . We say T to be minimum attaining if there exists a unit vector x P H 1 such that }T x} " mpT q, where mpT q :" inf t}T x} : x P H 1 , }x} " 1u is the minimum modulus of T . We say T to be absolutely minimum attaining (AM-operators in short), if for any closed subspace M of H 1 the restriction operator T | M : M Ñ H 2 is minimum attaining. In this paper, we give a new characterization of positive absolutely minimum attaining operators (AM-operators, in short), in terms of its essential spectrum. Using this we obtain a sufficient condition under which the adjoint of an AM-operator is AM. We show that a paranormal absolutely minimum attaining operator is hyponormal. Finally, we establish a spectral decomposition of normal absolutely minimum attaining operators. In proving all these results we prove several spectral results for paranormal operators. We illustrate our main result with an example.