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On Unitary N-dilations for Tuples of Circulant Contractions and von Neumann’s Inequality

American Journal of Computational Mathematics 2023年第4期13卷 594-606页

作者： Joachim Moussounda Mouanda Edwige Josette Maleka Koubemba Djagwa Dehainsala Mathematics Department Blessington Christian University Nkayi Republic of the Congo Mathematics Department N’Djamena University N’Djamena Tchad

We introduce the spectral mapping factorization of tuples of circulant matrices and its matrix version. We prove that every tuple of circulant contractions has a unitary N-dilation. We show that von Neumann’s inequality holds for tuples of circulant contractions. We construct completely contractive homomorphisms over the algebra of complex polynomials defined on .

关键词： dilations Polynomials Matrices

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Current status in the treatment options for esophageal achalasia

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World Journal of Gastroenterology 2013年第33期19卷 5421-5429页

作者： Seng-Kee Chuah Chien-Hua Chiu Wei-Chen Tai Jyong-Hong Lee Hung-I Lu Chi-Sin Changchien Ping-Huei Tseng Keng-Liang Wu Gastrointestinal Motility Unit Division of HepatogastroenterologyKaohsiung Chang Gung Memorial Hospitaland Chang Gung University College of Medicine Division of General Medicine Department of MedicineKaohsiung Chang Gung Memorial Hospitaland Chang Gung University College of Medicine Digestive Disease Center Department of Medical ResearchShow-Chwan Memorial Hospital Division of Thoracic and Cardiovascular Surgery Kaohsiung Chang Gung Memorial Hospital Department of Internal Medicine Graduate Institute of Clinical MedicineNational Taiwan University Hospital and College of MedicineNational Taiwan University

Recent advances in the treatment of achalasia include the use of high-resolution manometry to predict the outcome of patients and the introduction of peroral endoscopic myotomy(POEM).The first multicenter randomized,controlled,2-year follow-up study conducted by the European Achalasia Trial group indicated that laparoscopic Heller myotomy(LHM)was not superior to pneumatic dilations(PD).Publications on the long-term success of laparoscopic surgery continue to emerge.In addition,laparoscopic single-site surgery is applicable to advanced laparoscopic operations such as LHM and anterior fundoplication.The optimal treatment option is an ongoing matter of debate.In this review,we provide an update of the current progress in the treatment of esophageal achalasia.Unless new conclusive data prove otherwise,LHM is considered the most durable treatment for achalasia at the expense of increased reflux-associated complications.However,PD is the first choice for non-surgical treatment and is more costeffective.Repeated PD according to an"on-demand"strategy based on symptom recurrence can achieve long-term remission.Decision making should be based on clinical evidence that identifies a subcategory of patients who would benefit from specific treatment options.POEM has shown promise but its long-term efficacy and safety need to be assessed further.

关键词： Esophageal achalasia Endoscopic pneumatic dilations Botulinum injection Peroral endoscopic myotomy Minimally invasive Heller myotomy

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