Compact groups of positive operators on Banach lattices

In this paper, we study groups of positive operators on Banach lattices. If a certain factorization property holds for the elements of such a group, the group has a homomorphic image in the isometric positive operators which has the same invariant ideals as the original group. If the group is compact in the strong operator topology, it equals a group of isometric positive operators conjugated by a single central lattice automorphism, provided an additional technical assumption is satisfied, for which we have only examples. We obtain a characterization of positive representations of a group with compact image in the strong operator topology, and use this for normalized symmetric Banach sequence spaces to prove an ordered version of the decomposition theorem for unitary representations of compact groups. Applications concerning spaces of continuous functions are also considered.     

Equivalence after extension and Schur coupling coincide for inessential operators

In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE $?$ SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators.     

Synthesis and conformation of some 2,4-dioxa- and 2,4-dioxa-3-silabicyclo[3.3.1]nonanes

The conformation of the title compounds established by ¹³C and ¹H NMR spectroscopy shows that replacement of the 2- and 4-methylene groups in bicyclo[3.3.1]nonane by ether oxygen atoms strongly destablizes the cc conformation: in 2-oxabicyclo[3.3.1]-nonane the cc and the bc conformers are about equally populated, whereas in 2,4-dioxabicyclo[3.3.1]nonane the bc conformation predominates. The 2,4-dioxa-3-silabicyclo[3.3.1]nonanes also occur predominantly inthe bc conformation. As in the carbocyclic bicyclo[3.3.1]nonanes both wings are strongly flattened. A stereoselective synthesis of 3-methylbicyclo[3.3.1]nonane, an important model compound in this study, is described.     

The electron impact induced fragmentations of some 7-alkyl-3-oxabicyclo[3.3.1]nonanes

The mass spectra of a series of 7-alkyl substituted 3-oxabicyclo[3.3.1]nonanes are recorded. The fragmentation has been studied by the use of the metastable DADI and defocussing techniques. The character of the alkyl group is found to influence the fragmentation pattern. Stereoselective fragmentations for the 7-t-butyl derivatives are observed. In the endo-isomer, in contrast to the exo-isomer, a transannular hydrogen transfer plays a role.     

Jamming, yielding, and rheology of weakly vibrated granular media

We establish that the rheological curve of dry granular media is nonmonotonic, both in the presence and absence of external mechanical agitations. In the presence of weak vibrations, the nonmonotonic flow curves govern a hysteretic transition between slow but steady and fast, inertial flows. In the absence of vibrations, the nonmonotonic flow curve governs the yielding behavior of granular media. Finally, we show that nonmonotonic flow curves can be seen in at least two different flow geometries and for several granular materials.     

Zeolite ZSM-5 and related materials as catalyst in benzene chlorination

ZSM-5 type zeolites and related high siliceous materials induce addition of chlorine to benzene yielding hexachlorocyclohexanes, whereas Y-type zeolites favour substitution to yield chlorobenzenes.     

Riesz–Kantorovich formulas for operators on multi-wedged spaces

We introduce the notions of multi-suprema and multi-infima for vector spaces equipped with a collection of wedges, generalizing the notions of suprema and infima in ordered vector spaces. Multi-lattices are vector spaces that are closed under multi-suprema and multi-infima and are thus an abstraction of vector lattices. The Riesz decomposition property in the multi-wedged setting is also introduced, leading to Riesz–Kantorovich formulas for multi-suprema and multi-infima in certain spaces of operators.     

Conformational analysis of 7-alkyl-3-oxabicyclo-[3.3.1]nonanes and complexes with lanthanide shift reagents

The conformation of 3-oxabicyclo[3,3.1]nonane and of some of its 7α- and 7β-alkyl substituted derivatives has been studied with the use of ¹³C and ¹H NMR spectroscopy. A comparison is made with the carbocyclic analogues; it turns out that the replacement of the 3-methylene group by oxygen has no substantial influence on the conformational preferences. With the aid of ³J_HH coupling constants it is shown that the geometry of the cyclohexane rings is about the same as in the corresponding carbocyclic compounds. The results of calculations on the lanthanide induced shifts indicate that the tetrahydropyran ring is not flattened but probably somewhat puckered. The calculated location of Eu(III) in complexes of Eu(dpm)₃ with the 3-oxabicyclo [3.3.1]nonanes is compared with that in the complexes of the related compounds 2-oxaadamantane and 4-methyltetrahydropyran. The data indicate that the lanthanide ion coordinates “axially” to the latter compound.     

Denjoy-Wolff theorems for Hilbert’s and Thompson’s metric spaces

We study the dynamics of fixed point free mappings on the interior of a normal, closed cone in a Banach space that are nonexpansive with respect to Hilbert’s metric or Thompson’s metric. We establish several Denjoy-Wolff type theorems which confirm conjectures by Karlsson and Nussbaum for an important class of nonexpansive mappings. We also extend and put into a broader perspective results by Gaubert and Vigeral concerning the linear escape rate of such nonexpansive mappings.