On Fock covariance for product systems and the reduced Hao-Ng isomorphism problem by discrete actions

We provide a characterisation of equivariant Fock covariant injective representations for product systems. We show that this characterisation coincides with Nica covariance for compactly aligned product systems over right LCM semigroups of Kwa\'{s}niewski and Larsen, and with the Toeplitz representations of a discrete monoid of Laca and Sehnem. By combining with the framework established by Katsoulis and Ramsey, we resolve the reduced Hao-Ng isomorphism problem for generalised gauge actions by discrete groups.Comment: 37 page

Operator algebras associated with C *-dynamical systems and C *-correspondences

Η παρούσα διπλωματική εργασία αποσκοπεί στο να περιγράψει συγκεκριμένες άλγεβρες τελεστών που σχετίζονται με C*-δυναμικά συστήματα και C*-αντιστοιχίες. Εισάγουμε την έννοια του σταυρωτού γινομένου μιας C*-άλγεβρας με μια διακριτή ομάδα και περιγράφουμε αναλυτικά την ειδική περίπτωση που η διακριτή ομάδα είναι οι ακέραιοι. Δίνουμε ικανές και αναγκαίες συνθήκες στην περίπτωση όπου η C*-άλγεβρα είναι η άλγεβρα συνεχών συναρτήσεων ενός συμπαγούς Hausdorff τοπολογικού χώρου, ώστε το σταυρωτό γινόμενο να είναι απλή C*-άλγεβρα. Επιπλέον, εισάγουμε την έννοια του ημι-σταυρωτού γινομένου και δίνουμε εναλλακτικές περιγραφές της νόρμας του στην περίπτωση που το C*-δυναμικό σύστημα επάγεται από *-αυτομορφισμό. Επίσης, εισάγουμε την έννοια της C*-αντιστοιχίας και των αναπαραστάσεων της και αποδεικνύουμε το Gauge-Invariance Uniqueness Theorem. Τέλος, χρησιμοποιούμε αποτελέσματα και εργαλεία που έχουμε αναπτύξει στα προηγούμενα κεφάλαια ώστε να αποδείξουμε ότι το C*-envelope του ημι-σταυρωτού γινομένου είναι το σταυρωτό γινόμενο, στην περίπτωση C*-δυναμικού συστήματος που επάγεται από *-αυτομορφισμό και ότι το C*-envelope της Tensor algebra μιας C*-αντιστοιχίας είναι η Cuntz-Pimsner algebra.The aim of the present thesis is to describe certain operator algebras associated with C*-dynamical systems and C*-correspondences. We introduce the notion of the crossed product of a C*-algebra by a discrete group and we study in detail the case of the integers. We give necessary and sufficient conditions, when the C*-algebra is the algebra of continuous functions on a compact Hausdorff topological space, for the crossed product to be simple. Furthermore, we introduce the notion of the semi-crossed product and we give alternative descriptions of its norm when the C*-dynamical system is induced by a ∗-automorphism. In addition, we study C*-correspondences and their representations and we prove the Gauge-Invariance Uniqueness theorem. Finally, we use results and tools that we have developed so far, in order to identify the C*-envelope of the semi-crossed product and the C*-envelope of the tensor algebra of a C*-correspondence

Outcomes of elective liver surgery worldwide: a global, prospective, multicenter, cross-sectional study

Background: The outcomes of liver surgery worldwide remain unknown. The true population-based outcomes are likely different to those vastly reported that reflect the activity of highly specialized academic centers. The aim of this study was to measure the true worldwide practice of liver surgery and associated outcomes by recruiting from centers across the globe. The geographic distribution of liver surgery activity and complexity was also evaluated to further understand variations in outcomes. Methods: LiverGroup.org was an international, prospective, multicenter, cross-sectional study following the Global Surgery Collaborative Snapshot Research approach with a 3-month prospective, consecutive patient enrollment within January–December 2019. Each patient was followed up for 90 days postoperatively. All patients undergoing liver surgery at their respective centers were eligible for study inclusion. Basic demographics, patient and operation characteristics were collected. Morbidity was recorded according to the Clavien–Dindo Classification of Surgical Complications. Country-based and hospital-based data were collected, including the Human Development Index (HDI). (NCT03768141). Results: A total of 2159 patients were included from six continents. Surgery was performed for cancer in 1785 (83%) patients. Of all patients, 912 (42%) experienced a postoperative complication of any severity, while the major complication rate was 16% (341/2159). The overall 90-day mortality rate after liver surgery was 3.8% (82/2,159). The overall failure to rescue rate was 11% (82/ 722) ranging from 5 to 35% among the higher and lower HDI groups, respectively. Conclusions: This is the first to our knowledge global surgery study specifically designed and conducted for specialized liver surgery. The authors identified failure to rescue as a significant potentially modifiable factor for mortality after liver surgery, mostly related to lower Human Development Index countries. Members of the LiverGroup.org network could now work together to develop quality improvement collaboratives

On Fock covariance for product systems and the reduced Hao-Ng isomorphism problem by discrete actions

We provide a characterization of equivariant Fock covariant injective representations for product systems. We show that this characterization coincides with Nica covariance for compactly aligned product systems over right least common multiple semigroups of Kwaśniewski and Larsen and with the Toeplitz representations of a discrete monoid of Laca and Sehnem. By combining with the framework established by Katsoulis and Ramsey, we resolve the reduced Hao-Ng isomorphism problem for generalized gauge actions by discrete groups. © The Author(s), 2025

Pancreatic surgery outcomes: multicentre prospective snapshot study in 67 countries

Background: Pancreatic surgery remains associated with high morbidity rates. Although postoperative mortality appears to have improved with specialization, the outcomes reported in the literature reflect the activity of highly specialized centres. The aim of this study was to evaluate the outcomes following pancreatic surgery worldwide. Methods: This was an international, prospective, multicentre, cross-sectional snapshot study of consecutive patients undergoing pancreatic operations worldwide in a 3-month interval in 2021. The primary outcome was postoperative mortality within 90 days of surgery. Multivariable logistic regression was used to explore relationships with Human Development Index (HDI) and other parameters. Results: A total of 4223 patients from 67 countries were analysed. A complication of any severity was detected in 68.7 per cent of patients (2901 of 4223). Major complication rates (Clavien–Dindo grade at least IIIa) were 24, 18, and 27 per cent, and mortality rates were 10, 5, and 5 per cent in low-to-middle-, high-, and very high-HDI countries respectively. The 90-day postoperative mortality rate was 5.4 per cent (229 of 4223) overall, but was significantly higher in the low-to-middle-HDI group (adjusted OR 2.88, 95 per cent c.i. 1.80 to 4.48). The overall failure-to-rescue rate was 21 per cent; however, it was 41 per cent in low-to-middle- compared with 19 per cent in very high-HDI countries. Conclusion: Excess mortality in low-to-middle-HDI countries could be attributable to failure to rescue of patients from severe complications. The authors call for a collaborative response from international and regional associations of pancreatic surgeons to address management related to death from postoperative complications to tackle the global disparities in the outcomes of pancreatic surgery (NCT04652271; ISRCTN95140761)

Pancreatic surgery outcomes: multicentre prospective snapshot study in 67 countries

Background: Pancreatic surgery remains associated with high morbidity rates. Although postoperative mortality appears to have improved with specialization, the outcomes reported in the literature reflect the activity of highly specialized centres. The aim of this study was to evaluate the outcomes following pancreatic surgery worldwide.Methods: This was an international, prospective, multicentre, cross-sectional snapshot study of consecutive patients undergoing pancreatic operations worldwide in a 3-month interval in 2021. The primary outcome was postoperative mortality within 90 days of surgery. Multivariable logistic regression was used to explore relationships with Human Development Index (HDI) and other parameters.Results: A total of 4223 patients from 67 countries were analysed. A complication of any severity was detected in 68.7 percent of patients (2901 of 4223). Major complication rates (Clavien-Dindo grade at least IIIa) were 24, 18, and 27 percent, and mortality rates were 10, 5, and 5 per cent in low-to-middle-, high-, and very high-HDI countries respectively. The 90-day postoperative mortality rate was 5.4 per cent (229 of 4223) overall, but was significantly higher in the low-to-middle-HDI group (adjusted OR 2.88, 95 per cent c.i. 1.80 to 4.48). The overall failure-to-rescue rate was 21 percent; however, it was 41 per cent in low-to-middle-compared with 19 per cent in very high-HDI countries.Conclusion: Excess mortality in low-to-middle-HDI countries could be attributable to failure to rescue of patients from severe complications. The authors call for a collaborative response from international and regional associations of pancreatic surgeons to address management related to death from postoperative complications to tackle the global disparities in the outcomes of pancreatic surgery (NCT04652271; ISRCTN95140761)