It is folklore that a power bounded operator on a sequentially complete locally convex space generates a uniformly continuous C0-semigroup which is given by the corresponding power series representation. Recently, Domański asked if in this result the assumption of being power bounded can be relaxed. We employ conditions introduced by Żelazko to give a weaker but still sufficient condition for g...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

The bounded approximate version of $varphi$-amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded ap...

In this paper, we introduce two different notions of generalized supra soft sets namely supra A--soft sets and supra soft locally closed sets in supra soft topological spaces, which are weak forms of supra open soft sets and discuss their relationships with each other and other supra open soft sets [{it International Journal of Mathematical Trends and Technology} (IJMTT), (2014) Vol. 9 (1):37--...

In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...

We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators.

We prove that the generalized Benjamin-Ono equations ∂tu + H∂2 xu ± u ∂xu = 0, k ≥ 4 are locally well-posed in the scaling invariant spaces Ḣsk(R) where sk = 1/2 − 1/k. Our results also hold in the nonhomogeneous spaces Hsk(R). In the case k = 3, local well-posedness is obtained in Hs(R), s > 1/3.

In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.

We present some properties of real valued functions of bounded generalized variation of Riesz–Orlicz type including weight and characterize Lipschitzian superposition Nemytskii operators which map between spaces (in fact, Banach algebras) of these functions.