The Jacobi polynomials induce a translation operator on function spaces on the interval [−1, 1]. For any homogeneous Banach space B w.r.t. this translation, we can study the according little and big Lipschitz spaces, lipB(λ) and LipB(λ), respectively. The big Lipschitz spaces are not homogeneous themselves. Therefore we introduce semihomogeneous Banach spaces w.r.t. Jacobi translation, of which...

in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

It is proved that if a Köthe sequence space X is monotone complete and has the weakly convergent sequence coefficient WCS(X) > 1, then X is order continuous. It is shown that a weakly sequentially complete Köthe sequence space X is compactly locally uniformly rotund if and only if the norm in X is equi-absolutely continuous. The dual of the product space ( ⊕∞ i=1 Xi)Φ of a sequence of Banach sp...

The representation of linear operators, on the Banach space of Bochner integrable functions, has been the object of much study for the past fifty years. Dunford and Pettis began this investigation in 1940 with the representation of weakly compact and norm compact operators on L1(R) by a Bochner integral, see [6,8]. Andrews has extended their study to the case of the space L1(E), of E-valued, Bo...

We view regularized learning of a function in a Banach space from its finite samples as an optimization problem. Within the framework of reproducing kernel Banach spaces, we prove the representer theorem for the minimizer of regularized learning schemes with a general loss function and a nondecreasing regularizer. When the loss function and the regularizer are differentiable, a characterization...

We create a new family of Banach spaces, the James–Schreier spaces, by amalgamating two important classical Banach spaces: James’ quasi-reflexive Banach space on the one hand and Schreier’s Banach space giving a counterexample to the Banach–Saks property on the other. We then investigate the properties of these James–Schreier spaces, paying particular attention to how key properties of their ‘a...

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...

We show that if a separable Banach space Z contains isometric copies of every strictly convex separable Banach space, then Z actually contains an isometric copy of every separable Banach space. We prove that if Y is any separable Banach space of dimension at least 2, then the collection of separable Banach spaces which contain an isometric copy of Y is analytic non Borel.

The paper investigates the variation of the spectrum of operators in infinite dimensional Banach spaces. Consider the space of bounded operators on a separable Banach space when equipped with the strong operator topology, and the Polish space of compact subsets of the closed unit disc of the complex plane when equipped with the Hausdorff topology. Then, it is shown that the unit spectrum functi...

In this note we construct a C∞-smooth, LFC (Locally depending on Finitely many Coordinates) bump function, in every separable Banach space admitting a continuous, LFC bump function.