In [l], we proved a criterion for the disjointness of two induced representations UL and UM of a Lie group G, where L and M are finite-dimensional unitary representations of compact subgroups H and R, respectively, of G. The purpose of this paper is to improve this theorem by getting a stronger conclusion, while dropping the conditions that G be a Lie group and H be compact, and that L and M he...

In this paper, the denition of net-theoretical L-generalized convergencespaces is proposed. It is shown that, for L a frame, the category ofenriched L-fuzzy topological spaces can be embedded in that of L-generalizedconvergence spaces as a reective subcategory and the latter is a cartesianclosedtopological category.

recently, mohiuddine and alghamdi introduced the notion of lacunary statistical convergence in a locally solid riesz space and established some results related to this concept. in this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a tauberian theorem to the l...

The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications c space. first one produces sequential sc. second makes absolute c-convergence generalizes weak convergence. third modification unbounded various convergences recently studied in literature. last applicable whenever commu...

in this paper, the concept of {sl local base with  stratifiedstructure} in $i$-topological vector spaces is introduced. weprove that every $i$-topological vector space has a balanced localbase with stratified structure. furthermore, a newcharacterization of $i$-topological vector spaces by means of thelocal base with stratified structure is given.

For a family of weight functions that include the general Jacobi weight functions as special cases, exact condition for the convergence of the Fourier orthogonal series in the weighted L space is given. The result is then used to establish a Marcinkiewicz-Zygmund type inequality and to study weighted mean convergence of various interpolating polynomials based on the zeros of the corresponding o...