Isometries of sp(α)

The Mazur–Ulam property in ℓ∞-sum and c0-sum of strictly convex Banach spaces

Projections in the convex hull of three surjective isometries on [formula omitted

Tingley's problems on uniform algebras

Surjective isometries between some classical function spaces are investigated. We give a simple technical scheme which verifies whether any such isometry is given by a homeomorphism between corresponding Hausdorff compact spaces. In particular the answer is positive for the C 1 ( X ) {C^1}(X) , AC ⁡ [ 0 , 1 ] \operatorname {AC} [0,1] , Lip α ( X ) {\operatorname {Lip} _\alpha }(X) and lip α ( X ) {\operatorname {lip} _\alpha }(X) spaces provided with various natural norms.

A theorem on maximal monotonic sets in Hilbert space

The Hardy–Littlewood inequalities for m-linear forms on $$\ell _{p}$$ spaces are known just for $$p>m$$. The critical case $$p=m$$ was overlooked for obvious technical reasons and, up to now, the only known estimate is the trivial one. In this paper we deal with this critical case of the Hardy–Littlewood inequality. More precisely, for all positive integers $$m\ge 2$$ we have $$\begin{aligned} \sup _{j_{1}}\left( \sum _{j_{2}=1}^{n}\left( \ldots \left( \sum _{j_{m}=1} ^{n}\left| T\left( e_{j_{1}},\ldots ,e_{j_{m}}\right) \right| ^{s_{m} }\right) ^{\frac{1}{s_{m}}\cdot s_{m-1}}\ldots \right) ^{\frac{1}{s_{3}}s_{2} }\right) ^{\frac{1}{s_{2}}}\le 2^{\frac{m-2}{2}}\left\| T\right\| \end{aligned}$$for all m-linear forms $$T{:}\,\ell _{m}^{n}\times \cdots \times \ell _{m} ^{n}\rightarrow \mathbb {K}=\mathbb {R}$$ or $$\mathbb {C}$$ with $$s_{k} =\frac{2m(m-1)}{mk-2k+2}$$ for all $$k=2,\ldots ,m$$ and for all positive integers n. As a corollary, for the classical case of bilinear forms investigated by Hardy and Littlewood in 1934 our result is sharp in a strong sense (both exponents and constants are optimal for real and complex scalars).

Mathematical and statistical open source software (OSS) has played a vital and positive role in computing statistics, performing numerical computations, and solving for real and complex scalars. There is an enormous need to apply quality models to this type of software. In this paper, we present an inclusive set of current quality models and demonstrate their application to OSS. As very little research has been carried out on the quality in use assessment of mathematical software, this work investigates the application of the quality in use model inspired by ISO/IEC 25010 on three OSS products: Scilab, R-Language, and GNU Octave. We can confidently state that Scilab, R-Language, and GNU Octave perform similarly in terms of effectiveness, efficiency, productivity, and cognitive load. However, Scilab outperforms GNU Octave slightly when it comes to error safety.

A universal theorem for stability of ε-isometries of Banach spaces

In this paper, we consider linear spaces and algebras with real scalars. It is well known that if X is a Banach space and is the set of all bounded linear operators which map X into itself, then is a Banach algebra. In this paper we shall show that can be partially ordered so that it becomes a partially ordered algebra in which norm convergence is equivalent to order convergence. This motivates a study of Banach algebras of operators in which one uses the order structure to obtain various results. In addition, it encourages a study of partially ordered algebras in general, since our result shows that among such algebras one finds all real Banach algebras of operators. Of course, there are many other real algebras which are naturally partially ordered and which have been studied from that point of view.

A projection P0 on a complex Banach space is generalized 3- circular if its linear combination with two projections P1 and P2 having coefficients λ1 and λ2, respectively, is a surjective isometry, where λ1 and λ2 are distinct unit modulus complex numbers different from 1 and P0⊕P1⊕P2=I. Such projections are always contractive. In this paper, we prove structure theorems for generalized 3-circular projections acting on the spaces of all n×n symmetric and skew-symmetric matrices over C when these spaces are equipped with unitary congruence invariant norms.

Isometric shifts on [formula omitted

It has previously been shown that separable Banach spaces $V$ with trivial $L$-structure have the ${L^1}$-Banach-Stone property, i.e. every surjective isometry between two Bochner spaces ${L^1}({\mu _i},V)$ induces an isomorphism of the two measure algebras. We remove the separability restriction, employing the topology of the measure algebra’s Stonean space. The result is achieved via a complete description of the $L$-structure of ${L^1}(\mu ,V)$.

The Dual Complexity Space as the Dual of a Normed Cone

Some properties of the injective tensor product of Lp[0,1] and a Banach space

This paper proposes a video enhancement method using a novel super-resolution reconstruction (SRR) framework for real standard sequences that are corrupted by any noise models. The traditional SRR algorithms are very sensitive to their assumed model of data and noise, which limits their utility. The real noise models that corrupt the measure sequence are unknown; consequently, SRR algorithm using LI or L2 norm may degrade the image sequence rather than enhance it. The robust norm applicable to several noise and data models is desired in SRR algorithms. First, this paper proposes a robust SRR algorithm based on the stochastic regularization technique of Bayesian MAP estimation by minimizing a cost function. The Huber norm with Tikhonov regularization is used for measuring the difference between the projected estimate of the high-resolution image and each low resolution image, removing outliers in the data. Second, in order to cope with real sequences and complex motion sequences, this paper proposes an improved SRR observation model, affine block-based transform, devoted to the case of nonisometric inter-frame motion. The experimental results show that the proposed reconstruction can enhance real complex motion sequences, such as Suzie and Foreman sequence, and confirm the effectiveness of our algorithm and demonstrate its superiority to other SRR algorithms based on LI and L2 norm for several noise models such as AWGN, Poisson, Salt&Pepper and Speckle noise.