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Some characterizations of hereditary C ∗ C^* -subalgebras of weakly Rickart C ∗ C^* -algebras with weak ∗ ^* angelic dual balls are given. In particular, it turns out that weak ∗ ^* angelicity, weak ∗ ^* sequentiality and weak ∗ ^* sequential compactness of dual balls are the same on this class, and that they are characterized by using ideals of compact elements in those algebras. As an application, it is shown that a weakly Rickart C ∗ C^* -algebra has weak ∗ ^* angelic dual ball if and only if it coincides with the ideal of compact elements, which happens if and only if the algebra is finite dimensional.

We introduce and study modular Birkhoff–James orthogonality for typical Banach modules $$B({\mathbb {X}},{\mathbb {Y}})$$ and $$K({\mathbb {X}},{\mathbb {Y}}),$$ where $${\mathbb {X}}$$ and $${\mathbb {Y}}$$ are Banach spaces. We present some basic characterizations of modular Birkhoff–James orthogonality under certain restrictions, and completely characterize left symmetric points for the said orthogonality relation in $$B({\mathbb {X}},{\mathbb {Y}})$$ and $$K({\mathbb {X}},{\mathbb {Y}}).$$ The complications involved in an analogous study of right symmetric points are illustrated through concrete examples.

In this paper, complete characterizations of left (or right) symmetric points for strong Birkhoff orthogonality in$$B(\mathcal {H},\mathcal {K})$$B(H,K)and$$K(\mathcal {H},\mathcal {K})$$K(H,K)are given, where$$\mathcal {H},\mathcal {K}$$H,Kare complex Hilbert spaces and$$B(\mathcal {H},\mathcal {K})$$B(H,K)($$K(\mathcal {H},\mathcal {K})$$K(H,K)) is the space of all bounded linear (compact) operators from$$\mathcal {H}$$Hinto$$\mathcal {K}$$K.

Radon planes are two-dimensional real normed spaces in which Birkhoff(-James) orthogonality is symmetic. It is shown that every Radon plane is isometrically isomorphic to a special Day–James space generated by a pair of an absolute norm and its dual norm.

A Banach space X is said to be isomorphic to another Y with respect to the structure of Birkhoff-James orthogonality, denoted by X ∼ B J Y , if there exists a (possibly nonlinear) bijection between X and Y that preserves Birkhoff-James orthogonality in both directions. It is shown that X ≅ Y if either X or Y is finite dimensional and X ∼ B J Y , and that l p ≁ B J l q if 1 p q ∞ . Moreover, if H is a Hilbert space with dim ⁡ H ≥ 3 and H ∼ B J X , then H = X . In the two-dimensional case, it turns out that l p , q 2 ∼ B J l 2 2 , which indicates that nonlinear Birkhoff-James orthogonality preservers between Banach spaces are not necessarily scalar multiples of isometric isomorphisms.

In this paper, we give a complete description of left symmetric points for Birkhoff orthogonality in the preduals of von Neumann algebras. As a consequence, except for $\mathbb{C}$, $\ell _{\infty }^{2}$ and $M_{2}(\mathbb{C})$, there are no von Neumann algebras whose preduals have nonzero left symmetric points for Birkhoff orthogonality.

Complete characterizations of left or right symmetric points for (strong) Birkhoff orthogonality in von Neumann algebras and abelian unital C ⁎ -algebras are given. As an application, we show that every linear strong Birkhoff orthogonality preserver between von Neumann algebras is an algebraic ⁎-isomorphism.

Ethanol is considered as a renewable transport fuels and demand is expected to grow. In this work, trends related to bio-ethanol production are described using Thailand as an example. Developments on high-temperature fermentation and membrane technologies are also explained. This study focuses on the application of membranes in ethanol recovery after fermentation. A preliminary simulation was performed to compare different process configurations to concentrate 10 wt% ethanol to 99.5 wt% using membranes. In addition to the significant energy reduction achieved by replacing azeotropic distillation with membrane dehydration, employing ethanol-selective membranes can further reduce energy demand. Silicalite membrane is a type of membrane showing one of the highest ethanol-selective permeation performances reported today. A silicalite membrane was applied to separate a bio-ethanol solution produced via high-temperature fermentation followed by a single distillation. The influence of contaminants in the bio-ethanol on the membrane properties and required further developments are also discussed.

In this paper, we give an affirmative answer to Tingley's problem between finite von Neumann algebras. To do this, we see that every norm closed proper face of the unit ball of a unital C ⁎ -algebra can be represented as the intersection of a family of maximal proper faces.

In this paper, it is shown that every surjective isometry between the unit spheres of two finite dimensional C ⁎ -algebras extends to a real-linear Jordan ⁎-isomorphism followed by multiplication operator by a fixed unitary element. This gives an affirmative answer to Tingley's problem between two finite-dimensional C ⁎ -algebras. Moreover, we show that if two finite dimensional C ⁎ -algebras have isometric unit spheres, then they are ⁎-isomorphic.

A new class of triarylmethane-based phosphines (L1–L4) and their Pd(II) and Rh(I) complexes were synthesized and subsequently characterized by NMR spectroscopy and X-ray diffraction analysis. The reactions of these phosphines with [PdCl(π-allyl)]2 gave the square-planar Pd(II) complexes [PdCl(π-allyl)(L)] (L = L1–L4). The treatment of [PdCl(π-allyl)(L3)] and [PdCl(π-allyl)(L4)], which have CF3-substituted triarylmethane and 9-arylfluorene moieties, respectively, with LiOtBu afforded P,C(sp3)-chelated palladacycle complexes. Reversibility between a C(sp3)–M covalent bond and a C(sp3)–H···M interaction was experimentally demonstrated using [RhCl(nbd)]2 as a Rh(I) source. The triarylmethane-monophosphines L1–L4 were applied to the Pd-catalyzed 1,4-addition of arylboronic acids to enones.

A new notion of non-linear isomorphisms between Banach modules is introduced based on modular Birkhoff-James orthogonality. It is shown that a (possibly non-linear) bijective modular Birkhoff-James orthogonality preserver in both direction between spaces of continuous functions (vanishing at infinity) induces a homeomorphism between underlying locally compact Hausdorff spaces. Moreover, characterizations of linear and additive modular Birkhoff-James orthogonality preservers between spaces of continuous functions are also given in terms of the induced homeomorphisms and continuous functions having constant absolute values.

The class of two-dimensional normed spaces with James constant \({\sqrt{2}}\) is studied. It is shown that, if the norm is \({\pi/2}\)-rotation invariant, then its James constant is \({\sqrt{2}}\) if and only if the norm is \({\pi/4}\)-rotation invariant. We also present a characterization of \({\pi/4}\)-rotation invariant norms using some properties of certain convex functions on the unit interval, which allow us to easily construct norms the James constant of which are \({\sqrt{2}}\). Moreover, two important examples are given, which show that neither absoluteness, symmetry nor \({\pi/2}\)-rotation invariance can be a characteristic property of the norms with James constant \({\sqrt{2}}\).

In this paper, we study geometric structures and isometries of the unit sphere of n × n complex matrices. We introduce the notion of proper exposed points of the unit ball of a Banach space which provides a refinement of that of exposed point provided that the space is separable. As a new geometric interpretation of unitary matrices, it is shown that the set of all proper exposed points of the unit ball of M n ( C ) coincides with its unitary group U ( n ) , where M n ( C ) denotes the algebra of all n × n complex matrices. Moreover, we show that every maximal convex subset of the unit sphere of M n ( C ) can be identified with the unit ball of M n − 1 ( C ) by an affine bijection preserving the unitary matrices. This map is isometric with respect to any unitarily invariant norm. As an application, we completely determine the forms of surjective isometries on the unit sphere of M n ( C ) with respect to the operator norm, which provides an affirmative answer to Tingley's problem on M n ( C ) .

In this paper, we study the class of Banach spaces with James constant . It is shown that, for a Banach space of three or more dimensions, the James constant becomes if and only if the norm is induced by an inner product. Moreover, the symmetric absolute norms on with James constant are completely characterized in terms of convex functions on the unit interval, which provides many new examples of such norms other than the Euclidean or regular octagonal norms. However, it is also shown that there exist two-dimensional normed spaces with James constant outside of the family of symmetric absolute norms.

In this paper, we compare James and von Neumann–Jordan constants of normed spaces under certain conditions. It is shown that if a normed space with James constant $$\sqrt{2}$$ is three- or more dimensional, or is a $$\pi /2$$ -rotation-invariant two-dimensional space, then its von Neumann–Jordan constant is less than or equal to $$4-2\sqrt{2}$$ .

In this article, we study the (modified) von Neumann–Jordan constant and Zbăganu constant of $\pi/2$ -rotation invariant norms on $\mathbb{R}^{2}$ . Some estimations of these geometric constants are given. As an application, we construct various examples consisting of $\pi/2$ -rotation invariant norms.

The set of all absolute normalized norms on $\mathbb{R}^{2}$ (denoted by $AN_{2}$ ) has a convex structure with respect to the usual operation. In a previous article, N. Komuro, K.-S. Saito, and K.-I. Mitani calculated the James constants of $(\mathbb{R}^{2},\Vert \cdot\Vert )$ when $\Vert \cdot\Vert $ is an extreme point of $AN_{2}$ . In this article, we calculate the James constant of its dual space.

Let f : S(E) → S(B) be a surjective isometry between the unit spheres of two weakly compact JB*-triples not containing direct summands of rank smaller than or equal to 3. Suppose E has rank greater than or equal to 5. Applying techniques developed in JB*-triple theory, we prove that f admits an extension to a surjective real linear isometry T : E → B. Among the consequences, we show that every surjective isometry between the unit spheres of two compact C*-algebras A and B, without assuming any restriction on the rank of their direct summands (and in particular when A = K(H) and B = K(H′)), extends to a surjective real linear isometry from A into B. These results provide new examples of infinite-dimensional Banach spaces where Tingley’s problem admits a positive answer.