In this paper,we investigated the conditions of operators'dilated spuer-isometric.It is shown that the super-isometrically dilatable operator has a nontrivial invariant sub space, and it is proved,in addition,that for is unitarily equivalent to Mf if const.provided some abate condition is satisfied.
In this paper j a new theory on poilitwise quasi-uniformity is based on completelydistributive lattices.Properties of closure,locally basis, continuity etc.are discussed in inducedtopological molecular lattices. EaCh tOPological molecular lattice can be induced by a pot ̄isequasi-whfondty.Moreover,an equldsnt definition and a characterization of pseudDequasimetric in [8]are given.P seudth quas i- metrization theorem is obt anied.
In this paper,we apply the value distribution theory of Nevanlinna to solve the tence and possible number of meromorphic solutions of the differential equations with a domainative coefficient Pn or P0. At the same time,we give some examples to show that our results are sharp.