On Symmetric Spaces With Convergence in Measure on Reflexive Subspaces

A closed subspace H of a symmetric space X on [0, 1] is said to be strongly embedded in X if in H the convergence in X-norm is equivalent to the convergence in measure. We study symmetric spaces X with the property that all their reflexive subspaces are strongly embedded in X. We prove that it is the case for all spaces, which satisfy an analogue of the classical Dunford–Pettis theorem on relatively weakly compact subsets in L₁. At the same time the converse assertion fails for a broad class of separableMarcinkiewicz spaces.     

On stably -monotone Banach couples

The $ \vec E $ \vec E = (E, E(2^-k )) is a stably $ \vec E $ \vec E is $ \vec E $ \vec E is $ \vec E $ \vec E is -monotone, then either E = l _p (1 ≤ p < ∞) or E = c ₀.     

The Mo−OH proton of the low-pH form of sulfite oxidase: Comparison of the hyperfine interactions obtained from pulsed ENDOR, CW-EPR and ESEEM measurements

Pulsed electron nuclear double resonance (ENDOR) spectra have been obtained for the exchangeable Mo-OH proton of the low-pH form of native chicken liver sulfite oxidase (SO) and recombinant human SO for the first time. The spectra of the two enzymes are very similar, indicating a similar binding geometry of the hydroxyl ligand to the Mo center. The isotropic hyperfine interaction (hfi) constant for the proton of the OH ligand in both enzymes is about 26 MHz. The anisotropic components of the hfi obtained from the pulsed ENDOR spectra are about 1.6–1.8 times larger than those obtained by continuous-wave electron paramagnetic resonance and electron spin echo envelope modulation. These hfi differences are explained by a rotational disorder of the Mo-OH group. A similar rotational disorder of the coordinated exchangeable ligand has been found previously for the high-pH and phosphate-inhibited forms of SO.     

Disjointly strictly singular inclusions of symmetric spaces

In this paper, the disjoint strict singularity of inclusions of symmetric spaces of functions on an interval is considered. A condition for the presence of a “gap” between spaces sufficient for the inclusion of one of these spaces into the other to be disjointly strictly singular is found. The condition is stated in terms of fundamental functions of spaces and is exact in a certain sense. In parallel, necessary and sufficient conditions for an inclusion of Lorentz spaces to be disjointly strictly singular (and similar conditions for Marcinkiewicz spaces) are obtained and certain other assertions are proved. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 3–14, January, 1999.     

Rosenthal type inequalities for martingales in symmetric spaces

We establish inequalities similar to classical Rosenthal ones for sequences of martingale differences in general symmetric spaces. A central role is played by a predictable square variation of a martingale.     

Investigation of the coordination structures of the molybdenum(v) sites of sulfite oxidizing enzymes by pulsed EPR spectroscopy

Sulfite oxidizing enzymes (SOEs) are physiologically vital and occur in all forms of life. During the catalytic cycle the five-coordinate square-pyramidal oxo-molybdenum active site passes through the Mo(v) state, and intimate details of the structure can be obtained from pulsed EPR spectroscopy through the hyperfine interactions (hfi) and nuclear quadrupole interactions (nqi) of nearby magnetic nuclei (e.g., (1)H, (2)H, (17)O, (31)P) of the ligands. By employing spectrometer operational frequencies ranging from approximately 4 to approximately 32 GHz, it is possible to make the nuclear Zeeman interaction significantly greater than the hfi and nqi, and thereby simplify the interpretations of the spectra. The SOEs exhibit three general types of Mo(v) structures which differ in the number of nearby exchangeable protons (one, two or zero). The observed structure depends upon the organism, pH, anions in the medium, and method of reduction. One type of structure has a single exchangeable Mo-OH proton approximately in the equatorial plane and a large isotropic hfi (e.g., low pH form of chicken SOE, low pH form of plant SOE reduced by Ti(iii)); the second type has two exchangeable protons with distributed orientations out of the equatorial plane and very small (or zero) isotropic hfi (e.g., high pH form of chicken SOE, high pH form of plant SOE reduced by sulfite); the third type has no nearby exchangeable protons and a coordinated oxyanion (e.g., phosphate inhibited chicken SOE, low pH form of plant SOE reduced by sulfite). An additional structural conclusion is that the orientation angle of any exchangeable equatorial ligand (OH, OH(2), PO(4)(3-)) is not uniquely fixed, but is distributed around its central value by up to +/-20 degrees (depending on pH, the type of the ligand and the type of enzyme). An unexpected finding was that the axial oxo group of SOEs exchanges with (17)O in solutions enriched in H(2)(17)O. The first determination of oxo (17)O nqi parameters for a well-characterized model compound, [Mo(17)O(SPh)(4)](-), clearly demonstrated that (17)O nqi parameters can distinguish between oxo and OH(2) ligands.