In the first part of the paper we study some properties of eigenelements of linear selfadjoint pencils Lu = λBu. In the second part we apply these results to the investigation of some boundary value problems for mixed type second order operator-differential equations.
Some properties of monotone type multivalued operators including accretive operators and the duality mapping are studied in connection with the structure of Banach spaces.
Let T be a continuous linear operator on a Hausdorff topological vector space 𝓧 over the field ℂ. We show that if T is N-supercyclic, i.e., if 𝓧 has an N-dimensional subspace whose orbit under T is dense in 𝓧, then T* has at most N eigenvalues (counting geometric multiplicity). We then show that N-supercyclicity cannot occur nontrivially in the finite-dimensional setting: the orbit of an N-dimensional subspace cannot be dense in an (N+1)-dimensional space. Finally, we show that a subnormal operator...
First, a result of J. W. Schmidt about the monotone enclosure of solutions of nonlinear equations is generalized. Then an iteration method is considered, which is more effective than other known methods. For this method, monotone enclosure statements are also proved.