Normalizers of Irreducible Subfactors

We consider normalizers of an irreducible inclusion $N\subseteq M$ of $\mathrm{II}_1$ factors. In the infinite index setting an inclusion $uNu^*\subseteq N$ can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these normalizers of $N$ in $M$ to projections in the basic construction and show that every trace one projection in the relative commutant $N'\cap$ is of the form $u^*e_Nu$ for some unitary $u\in M$ with $uNu^*\subseteq N$. This enables us to identify the normalizers and the algebras they generate in several situations. In particular each normalizer of a tensor product of irreducible subfactors is a tensor product of normalizers modulo a unitary. We also examine normalizers of irreducible subfactors arising from subgroup--group inclusions $H\subseteq G$. Here the normalizers are the normalizing group elements modulo a unitary from $L(H)$. We are also able to identify the finite trace $L(H)$-bimodules in $\ell^2(G)$ as double cosets which are also finite unions of left cosets.Comment: 33 Page

A remark on the similarity and perturbation problems

In this note we show that Kadison's similarity problem for C*-algebras is equivalent to a problem in perturbation theory: must close C*-algebras have close commutants?Comment: 6 Pages, minor typos fixed. C. R. Acad. Sci. Canada, to appea

Kadison-Kastler stable factors

A conjecture of Kadison and Kastler from 1972 asks whether sufficiently close operator algebras in a natural uniform sense must be small unitary perturbations of one another. For n≥3 and a free, ergodic, probability measure-preserving action of SL<sub>n</sub>(Z) on a standard nonatomic probability space (X,μ), write M=(L<sup>∞</sup>(X,μ)⋊SL<sub>n</sub>(Z))⊗¯¯¯R, where R is the hyperfinite II1-factor. We show that whenever M is represented as a von Neumann algebra on some Hilbert space H and N⊆B(H) is sufficiently close to M, then there is a unitary u on H close to the identity operator with uMu∗=N. This provides the first nonamenable class of von Neumann algebras satisfying Kadison and Kastler’s conjecture. We also obtain stability results for crossed products L<sup>∞</sup>(X,μ)⋊Γ whenever the comparison map from the bounded to usual group cohomology vanishes in degree 2 for the module L<sup>2</sup>(X,μ). In this case, any von Neumann algebra sufficiently close to such a crossed product is necessarily isomorphic to it. In particular, this result applies when Γ is a free group

Agarose drop method for loading thin polyacrylamide gels

The gels (<1 mm) can be loaded conveniently, rapidly, and quantitatively by suspending the sample to be analyzed in a drop of agarose gel and simply placing the solidified drop on top of the stacking gel. With this method there is no lower limit to the size of the sample to be loaded or to the thinness of the gel to be employed. Using the silver stain quantitation of between 1 and 1000 ng/sample is easily achieved.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23819/1/0000058.pd

Uromucoid (Tamm-Horsfall glycoprotein) forms different polymeric arrangements on a filter surface under different physicochemical conditions

Normal human urine cannot be forced through a 0.2 [mu]m filter. To investigate the reason for this phenomenon, uromucoid (Tamm-Horsfall protein) was purified from human urine and its capacity to block a 0.2 [mu]m Millipore filter was measured under different conditions. In the presence of cations (H+, Na+, Ca2+) uromucoid blocked the filter. The blocking varied with cation concentration. Scanning electron microscopy of the filter surface revealed different arrangements of polymerized uromucoid coating the filter surface depending on ionic conditions. In the presence of 100 mmol/l NaCl or 1 mmol/l CaCl2 uromucoid polymers were present in a fibrous arrangement. In the presence of both NaCl and CaCl2 a dence mat of uromucoid polymers was present together with clumps of aggregated polymer. In the absence of ions uromucoid formed a homogeneous coat on the filter surface (as demonstrated by scanning electron microscopy, Western blotting and 125I-uromucoid binding studies) but did not block the filter. Similar fibrous and highly aggregated arrangements of uromucoid polymer were seen in hyaline casts from urine. These data are consistent with the concept that the uromucoid glycoprotein can exist in several different polymeric forms under different ionic conditions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26802/1/0000358.pd

Contrast‐Enhanced Diagnostic Ultrasound Causes Renal Tissue Damage in a Porcine Model

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135402/1/jum201029101391.pd

A map of urine proteins based on one-dimensional SDS-polyacrylamide gel electrophoresis and Western blotting using one microliter of unconcentrated urine

A sensitive one-dimensional SDS-polyacrylamide gel electrophoretic system was devised whereby the proteins in 1 [mu]l of unconcentrated urine could be visualized by silver staining over the range 9 000-900 000 molecular weight. Identification of urine proteins was confirmed by Western blotting using peroxidase labelled antibodies. A map of the major proteins visualized in urine from individuals with renal disease was constructed. We conclude that the information available from the simple analysis of proteins according to their size is limited to general conclusions regarding whether proteinuria is likely to be of tubular or glomerular or mixed origin. More specific identification of individual proteins is not feasible because simple protein staining is not sufficiently reliable to identify individual proteins. The reasons for this conclusion are as follows: (a) many proteins in urine migrate with similar apparent molecular weights, (b) some proteins are not visualized by silver staining, and (c) albumin polymeric complexes and fragments can be present at almost any molecular weight. However, one-dimensional SDS-polyacrylamide gel electrophoresis together with Western blotting does provide reliable information which might be clinically and experimentally useful.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26100/1/0000176.pd

Normalisers of irreducible subfactors

We consider normalizers of an infinite index irreducible inclusion Nsubset of or equal toM of II1 factors. Unlike the finite index setting, an inclusion uNu*subset of or equal toN can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these one-sided normalizers of N in M to projections in the basic construction and show that every trace one projection in the relative commutant N′∩left angle bracketM,eNright-pointing angle bracket is of the form u*eNu for some unitary uset membership, variantM with uNu*subset of or equal toN generalizing the finite index situation considered by Pimsner and Popa. We use this to show that each normalizer of a tensor product of irreducible subfactors is a tensor product of normalizers modulo a unitary. We also examine normalizers of infinite index irreducible subfactors arising from subgroup–group inclusions Hsubset of or equal toG. Here the one-sided normalizers arise from appropriate group elements modulo a unitary from L(H). We are also able to identify the finite trace L(H)-bimodules in ℓ2(G) as double cosets which are also finite unions of left cosets

Polymeric complexes and fragments of albumin in normal human plasma

Nitrocellulose blots of normal human plasma proteins separated by sodium dodecyi sulfate-polyacrylamide gel electrophoresis were examined for polymeric complexes and fragments of albumin using an immunoperoxidase-labelled mouse monoclonal anti-human albumin antibody. Under reducing conditions, no polymeric complexes were seen. Under non-reducing conditions, polymeric complexes were detected at the following molecular weights: 210000, 168000, 147000, 132000, and 110000. These probably represent both homo- and heteropolymers of albumin. Fresh plasma samples were also analyzed by S-200 chromatography with the same results indicating that detection of polymeric complexes was not an artifact of the sodium dodecyl sulfate-polyacrylamide gel electrophoresis technique. In quantitative terms, polymeric complexes constituted 0.3-2.8% of the total albumin present. Fragments of albumin were also seen in normal human plasma with molecular weights of 45000, 28000 and 19000. These fragments probably represent breakdown products of albumin in normal blood, and they constituted less than 2% of the total albumin present.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/24635/1/0000046.pd