Escaping a neighborhood along a prescribed sequence in Lie groups and Banach algebras

It is shown that Jamison sequences, introduced in 2007 by Badea and Grivaux, arise naturally in the study of topological groups with no small subgroups, of Banach or normed algebra elements whose powers are close to identity along subsequences, and in characterizations of (self-adjoint) positive operators by the accretiveness of some of their powers. The common core of these results is a description of those sequences for which non-identity elements in Lie groups or normed algebras escape an arbitrary small neighborhood of the identity in a number of steps belonging to the given sequence. Several spectral characterizations of Jamison sequences are given, and other related results are proved

Summary report of the Standards, Options and Recommendations for the management of patients with non-small-cell lung carcinoma (2000)

SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Long-term survival of cancer patients compared to heart failure and stroke: A systematic review

<p>Abstract</p> <p>Background</p> <p>Cancer, heart failure and stroke are among the most common causes of death worldwide. Investigation of the prognostic impact of each disease is important, especially for a better understanding of competing risks. Aim of this study is to provide an overview of long term survival of cancer, heart failure and stroke patients based on the results of large population- and hospital-based studies.</p> <p>Methods</p> <p>Records for our study were identified by searches of Medline via Pubmed. We focused on observed and relative age- and sex-adjusted 5-year survival rates for cancer in general and for the four most common malignancies in developed countries, i.e. lung, breast, prostate and colorectal cancer, as well as for heart failure and stroke.</p> <p>Results</p> <p>Twenty studies were identified and included for analysis. Five-year observed survival was about 43% for all cancer entities, 40-68% for stroke and 26-52% for heart failure. Five-year age and sex adjusted relative survival was 50-57% for all cancer entities, about 50% for stroke and about 62% for heart failure. In regard to the four most common malignancies in developed countries 5-year relative survival was 12-18% for lung cancer, 73-89% for breast cancer, 50-99% for prostate cancer and about 43-63% for colorectal cancer. Trend analysis revealed a survival improvement over the last decades.</p> <p>Conclusions</p> <p>The results indicate that long term survival and prognosis of cancer is not necessarily worse than that of heart failure and stroke. However, a comparison of the prognostic impact of the different diseases is limited, corroborating the necessity for further systematic investigation of competing risks.</p

Frequent hypercyclicity, chaos, and unconditional Schauder decompositions

We prove that if X is any complex separable infinite-dimensional Banach space with an unconditional Schauder decomposition, X supports an operator T which is chaotic and frequently hypercyclic. This result is extended to complex Frechet spaces with a continuous norm and an unconditional Schauder decomposition, and also to complex Frechet spaces with an unconditional basis, which gives a partial positive answer to a problem posed by Bonet. We also solve a problem of Bes and Chan in the negative by presenting hypercyclic, but non-chaotic operators on \mathbb{C}^\mathbb{N}. We extend the main result to C_0-semigroups of operators. Finally, in contrast with the complex case, we observe that there are real Banach spaces with an unconditional basis which support no chaotic operator.This work was partially supported by ANR-Projet Blanc DYNOP, by the MEC and FEDER Projects MTM2007-64222 and MTM2010-14909, and by Generalitat Valenciana Project PROMETEO/2008/101.De La Rosa Penilla, M.; Frerick, L.; Grivaux, S.; Peris Manguillot, A. (2012). Frequent hypercyclicity, chaos, and unconditional Schauder decompositions. Israel Journal of Mathematics. 190(1):389-399. https://doi.org/10.1007/s11856-011-0210-6S3893991901S. Ansari, Existence of hypercyclic operators on topological vector spaces, Journal of Functional Analysis 148 (1997), 384–390.F. Bayart and S. Grivaux, Frequently hypercyclic operators, Transactions of the American Mathematical Society 358 (2006), 5083–5117.F. Bayart and S. Grivaux, Hypercyclicity and unimodular point spectrum, Journal of Functional Analysis 226 (2005), 281–300.F. Bayart and S. Grivaux, Invariant Gaussian measures for linear operators on Banach spaces and linear dynamics, Proceedings of the London Mathematical Society 94 (2007), 181–210.F. Bayart and É. Matheron, Dynamics of Linear Operators, Cambridge University Press, Cambridge, 2009.L. Bernal-González, On hypercyclic operators on Banach spaces, Proceedings of the American Mathematical Society 127 (1999), 1003–1010.J. Bès and A. Peris, Hereditarily hypercyclic operators, Journal of Functioanl Analysis 167 (1999), 94–112.J. Bonet, F. Martínez-Giménez and A. Peris, A Banach space wich admits no chaotic operator, The Bulletin of the London Mathematical Society 33 (2001), 196–198.M. De la Rosa, L. Frerick, S. Grivaux and A. Peris, Chaos on Fréchet spaces with unconditional basis, preprint.W. T. Gowers, A solution to Banach’s hyperplane problem, The Bulletin of the London Mathematical Society 26 (1994), 523–530.W. T. Gowers and B. Maurey, Banach spaces with small spaces of operators, Mathematische Annalen 307 (1997), 543–568.W. T. Gowers and B. Maurey, The unconditional basic sequence problem, Journal of the American Mathematical Society 6 (1993), 851–874.S. Grivaux, A new class of frequently hypercyclic operators, Indiana University Mathematics Journal, to appear.K. G. Grosse-Erdmann and A. Peris, Linear Chaos, Springer-Verlag, Berlin, 2011.K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monographs, New Series, Vol. 20, Clarendon Press, Oxford, 2000.S. Shkarin, On the spectrum of frequently hypercyclic operators, Proceedings of the American Mathematical Society 137 (2009), 123–134

Recurrence of paraneoplastic membranous glomerulonephritis following chemoradiation in a man with non-small-cell lung carcinoma

Membranous glomerulonephritis can occur as a rare paraneoplastic complication of human cancers. In this case report, we describe a patient who presented acutely with symptoms of the nephrotic syndrome including heavy proteinuria and anasarca. He was subsequently diagnosed with membranous glomerulonephritis, and soon afterwards was found to have stage IIIB non-small cell lung cancer. Following chemoradiation therapy, both the patient’s cancer and membranous glomerulonephritis dramatically improved. However, approximately 14 months following his initial presentation, the patient was found to have a recurrence of his nephrotic-range proteinuria which corresponded temporally with recurrence of his cancer. We present details of the case and a review of the relevant scientific literature

Disjoint mixing operators

AbstractChan and Shapiro showed that each (non-trivial) translation operator f(z)↦Tλf(z+λ) acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing