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We prove that any bijective map between the positive definite cones of von Neumann algebras which preserves a certain unitarily invariant norm of a particular weighted geometric mean of elements is essentially (up to two-sided multiplication by an invertible positive element) equal to the restriction of a Jordan *-isomorphism between the algebras.

Benralizumab is a humanised, anti-interleukin 5 receptor α monoclonal antibody that directly and rapidly depletes eosinophils, reduces asthma exacerbations, and improves lung function for patients with severe eosinophilic asthma. The objective of this trial was to assess the safety and efficacy of benralizumab for patients with mild to moderate, persistent asthma.

In this paper we describe the structure of surjective isometries of the space of all generalized probability distribution functions on ℝ with respect to the Kolmogorov-Smirnov metric.

As a consequence of the main result of the paper we obtain that every 2-local isometry of the $C^*$-algebra $B(H)$ of all bounded linear operators on a separable infinite-dimensional Hilbert space $H$ is an isometry. We have a similar statement concerning the isometries of any extension of the algebra of all compact operators by a separable commutative $C^*$-algebra. Therefore, on those $C^*$-algebras the isometries are completely determined by their local actions on the two-point subsets of the underlying algebras. AMS 2000 Mathematics subject classification: Primary 47B49

Let Hbe a separable infinite-dimensional complex Hilbert space. We prove that every continuous 2-local automorphism of the poset (that is, partially ordered set) of all idempotents on His an automorphism. Similar results concerning the orthomodular poset of all projections and the Jordan ring of all selfadjoint operators on Hwithout the assumption on continuity are also presented.

Abstract:: In this paper we characterize the automorphisms of Hilbert space effect algebras by means of their preserving properties which concern certain relations and quantities appearing in quantum measurement theory.

Abstract:: Wigner's classical theorem on symmetry transformations plays a fundamental role in quantum mechanics. It can be formulated, for example, in the following way: Every bijective transformation on the set ℒ of all 1-dimensional subspaces of a Hilbert space H which preserves the angle between the elements of ℒ is induced by either a unitary or an antiunitary operator on H. The aim of this paper is to extend Wigner's result from the 1-dimensional case to the case of n-dimensional subspaces of H with n∈ℕ fixed.

Wigner's theorem on symmetry transformations can be formulated in the followingway. If φ is a bijective map on the set of all nonzero minimal projections in atype I factor Awhich preserves transition probabilities with respect to a faithfulnormal semifinite trace, then it can be extended to a linear *-automorphism orto a linear *-antiautomorphism of A. In this paper we prove a natural analogueof this statement for type II factors.

Abstract: We present a generalization of Wigner's unitary-antiunitary theorem for pairs of ray transformations. As a particular case, we get a new Wigner-type theorem for non-Hermitian indefinite inner product spaces.

The set of all effects on a Hilbert space has an affine structure (it is a convex set) as well as a multiplicative structure (it can be equipped with the so-called Jordan triple product). In this paper we describe the corresponding automorphisms of that set.

Abstract. The aim of this paper is to solve a linear preserver problem on the function algebra C(X). We show that in the case in which X is a first countable compact Hausdorff space, every linear bijection $\phi :C(X)\to C(X)$ having the property that $\hbox {diam} (\phi (f)(X))=\hbox {diam} (f(X)) (f\in C(X))$ is of the form¶¶$ \phi (f)=\tau \cdot f\circ \varphi +t(f)1 \,\, (f\in C(X))$¶¶where $\tau \in {\Bbb C}, |\tau |=1, $\varphi :X\to X$ is a homeomorphism and $t:C(X)\to {\Bbb C}$ is a linear functional.

The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), Hbeing a separable infinite-dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively, every local surjective isometry, ofC0(R)⊗B(H) is an automorphism, respectively, a surjective isometry.

Abstract. In this paper we give the general form of order isomorphisms and that of triple isomorphisms of standard operator algebras. For any Schatten- von Neumann class of compact operators as well as for the whole operator algebra, it is proved that the group of all of its order automorphisms is reflexive in the algebra of all linear (not necessarily continuous) selfmaps of the underlying operator algebra. A similar reflexivity result concerning triple automorphisms of an arbitrary operator ideal is also presented.

The aim of this note is to characterize the cyclic and the irreducible $ ^*$ -algebra.

LetH be a separable infinite-dimensional complex Hilbert space. We prove that if ?: B(H)?B(H) is a*-preserving ring homomorphism whose range contains a rank-one operator and an operator with dense range, then ? is an isometric linear or conjugate-linear algebra automorphism of B(H). In particular, if the unilateral shift is contained in the range of a*-endomorphism ? of B(H), then ? is bijective.

There were five cases of Solitary papillomas and three of chronic infectious papillomatosis induced by a foreign body, one caused by broncholithiasis. The five isolated papillomas had verrucous appearances. The common opinion, that the solitary papilloma is likely to be a pedunculary tumor, seems untrue. Squamous or cylindric epithelium covering the same tumor may vary from region to region. We believe that multiple polyps caused by inhalation of hot, burning, and corrosive gases are of inflammatory origin. Once the causative factor (eg, a late diagnosed foreign body) is removed, the inflammatory papillomatosis may resolve spontaneously. After the removal of a benign papilloma, recurrence is usually caused by lack of operative radically rather than by malignancy. Laser technique and other coagulation methods make it possible to remove most tumors by performing bronchoscopy with only litde risk. Papillomas showing the signs of atypia and peribronchial spreading require later surgery.