Decay spectrum and decay subspace of normal operators

Let A be a self-adjoint operator on a Hilbert space. It is well known that A admits a unique decomposition into a direct sum of three self-adjoint operators A(p), A(ac) and A(sc) such that there exists an orthonormal basis of eigenvectors for the operator A(p) the operator A(ac) has purely absolutely continuous spectrum and the operator A(sc) has purely singular continuous spectrum. We show the existence of a natural further decomposition of the singular continuous component A c into a direct sum of two self-adjoint operators A(sc)(D) and A(sc)(ND). The corresponding subspaces and spectra are called decaying and purely non-decaying singular subspaces and spectra. Similar decompositions are also shown for unitary operators and for general normal operators.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

A new monoclonal antibody, P2A8(6), that specifically recognizes a novel epitope on the multidrug resistance-associated protein 1 (MRP1), but not on MRP2 nor MRP3

Multidrug resistance (NIDR) is a major problem in the chemotherapeutic treatment of cancer. Overexpression of the multidrug resistance-associated protein 1 (MRP1), is associated with NIDR in certain tumors. A number of MRP1-specific MAbs, which facilitate both clinical and experimental investigations of this protein, are available. To add to this panel of existing antibodies, we have now generated an additional MRP1-specific monoclonal antibody (MAb), P2A8(6), which detects a unique heat stable epitope on the MRP1 molecule. Female Wistar rats were immunized via footpad injections with a combination of two short synthetic peptides corresponding to amino acids 235-246 (peptide A) and 246-260 (peptide B) of the MRP1 protein. Immune reactive B cells were then isolated from the popliteal lymph nodes for fusion with SP2/O-Ag14 myeloma cells. Resultant hybridoma supernatants were screened for MRP1-specific antibody production. Antibody P2A8(6) was characterized by Western blotting and immunocytochemistry on paired multidrug resistant (MRP1 overexpressing) and sensitive parental cell lines. The antibody detects a protein of 190 kDa in MRP1-expressing cell lines but not in MRP2- or MRP3-transfected cell lines. P2A8(6) stains drug-selected and MRP1-transfected cell lines homogeneously by immunocytochemistry and recognizes MRP1 by immunohistochemistry on formalin-fixed paraffin wax-embedded tissue sections. Peptide inhibition studies confirm that P2AS(6) reacts with peptide B (amino acids 246-260), therefore recognizing a different epitope from that of all currently available MRP1 MAbs. This new MAb, chosen for its specificity to the MRP1 protein, may be a useful addition to the currently available range of MRP1-specific MAbs.

Selection with melphalan or paclitaxel (Taxol) yields variants with different patterns of multidrug resistance, integrin expression and in vitro invasiveness

A melphalan-resistant variant (Roswell Park Memorial Institute (RPMI)-2650M1) and a paclitaxel-resistant variant (RPMI-1650Tx) of the drug-sensitive human nasal carcinoma cell line, RPMI-2650. were established. The multidrug resistance (MDR) phenotype in the RPMI-2650Tx appeared to be P-glycoprotein (PgP)-mediated. Overexpression of multidrug resistant protein (MRP) family members was observed in the RPMI-2650M1 cells, which were also much more invasive in vitro than the parental cell line or the paclitaxel-resistant variant. Increased expression of alpha (2), alpha (5), alpha (6), beta (1) and beta (4) integrin subunits, decreased expression of alpha (4) integrin subunit, stronger adhesion to collagen type IV, laminin, fibronectin and matrigel, increased expression of MMP-2 and MMP-9 and significant motility compared with the parental cells were observed, along with a high invasiveness in the RPMI-7650M1 cells. Decreased expression of the alpha (2) integrin subunit, decreased attachment to collagen type IV, absence of cytokeratin 18 expression, no detectable expression of gelatin-degrading proteases and poor motility may be associated with the non-invasiveness of the RPMI-2650Tx variant. These results suggest that melphalan exposure can result in not only a MDR phenotype. but could also make cancer cells more invasive, whereas paclitaxel exposure resulted in MDR without increasing the in vitro invasiveness in the RPMI-2650 cells. (C) 2001 Elsevier Science Ltd. All rights reserved.

Stress resistance and disease resistance in seaweeds: The role of reactive oxygen metabolism

It has become clear over the last 15-20 years that the immediate effect of a wide range of environmental stresses, and of infection, on vascular plants is to increase the formation of reactive oxygen species (ROS) and to impose oxidative stress on the cells. Since 1994, sufficient examples of similar responses in a broad range of marine macroalgae have been described to show that reactive oxygen metabolism also underlies the mechanisms by which seaweeds respond (and become resistant) to stress and infection. Desiccation, freezing, low temperatures, high light, ultraviolet radiation, and heavy metals all tend to result in a gradual and continued buildup of ROS because photosynthesis is inhibited and excess energy results in the formation of singlet oxygen. The response to other stresses (infection or oligosaccharides which signal that infection is occurring, mechanical stress, hyperosmotic shock) is quite different-a more rapid and intense, but short-lived production of ROS, described as an