A generalized Young inequality and some new results on fractal space     Dfractal  real line number system  fractional set  generalized Young inequality       font style='font-size:12px;'> 2011/9/21

Abstract: Starting with real line number system based on the theory of the Yang's fractional set, the generalized Young inequality is established. By using it some results on the generalized inequalit...

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A complete locally convex space of countable dimension admitting an operator with no invariant subspaces      Cyclic operators  invariant subspaces  topological vector spaces       font style='font-size:12px;'> 2010/12/6

We construct a complete locally convex topological vector space X of countable algebraic dimension and a continuous linear operator T : X → X such that T has no non-trivial closed invariant subspaces.

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Effective construction of a class of positive operators in Hilbert space, which do not admit triangular factorization      Triangular operators  nest algebra  multiplicity 1  hyperin-transitive operator       font style='font-size:12px;'> 2010/12/2

A class of non-factorable positive operators is constructed. As a result,pure existence theorems in the well-known problems by Ringrose,Kadison and Singer are substituted by concrete examples.

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