Seminar za analizu i primene, 14. decembar 2023.

Naredni sastanak Seminara biće održan onlajn u četvrtak 14. decembra 2023. sa početkom u 16 časova

Predavač: dr Michael Frank, Leipzig University of Technology, Economics and Culture Faculty of Computer Science and Media
 
Naslov predavanja: REGULARITY RESULTS FOR CLASSES OF HILBERT C*-MODULES WITH RESPECT TO SPECIAL BOUNDED MODULAR FUNCTIONALS
 
Apstrakt:
Considering the deeper reasons of the appearance of a remarkable counterexample by J. Kaad and M. Skeide [17] we consider situations in which two Hilbert C*-modules M ⊂ N with M⊥ = {0} over a fixed C*-algebra A of coefficients cannot be separated by a non-trivial bounded A-linear functional r0 : N → A vanishing on M.  In other words, the uniqueness of extensions of the zero functional from M to N is focused.  We show this uniqueness of extension for any such pairs of Hilbert C*-modules over W*-algebras, over monotone complete C*-algebras and over compact C*-algebras. Moreover, uniqueness of  extension takes place also for any one-sided maximal modular ideal of any C*-algebra. Such a non-zero separating bounded A-linear functional r0 exist for a given pair of Hilbert C*-modules  M ⊆ N over a given C*-algebra A iff there exists a bounded A-linear non-adjointable operator  T0 : N → N such that the kernel of T0 is not biorthogonally closed w.r.t. N and contains M.  This is a new perspective on properties of bounded modular operators that might appear in  Hilbert C* module theory. By the way, we find a correct proof of [13, Lemma 2.4] in the case of monotone  complete and compact C*-algebras, but not in the general C*-case. Some ideas published by V. M. Manuilov in [31] need a thorough revision.  In the particular case, when N is the multiplier module of M both these modules might not coincide, but the orthogonal complement of M in N = V (M) equals to zero. One has an isometric inclusion of N0 into M0, sometimes even N0 ⊂ M0. So, non-trivial extensions of the zero modular functional on M to a non trivial bounded modular functional on N = V (M) vanishing on M cannot exist.

Napomena: Registracija za učešće na seminaru je dostupna na sledećem linku:
https://miteam.mi.sanu.ac.rs/asset/LKGS835QQhi4x5uGw

Ukoliko ste već registrovani, predavanja možete pratiti na sledećem linku (nakon što se ulogujete): https://miteam.mi.sanu.ac.rs/asset/5dTX9wSbARfwfpNY5

Neulogovani korisnici mogu pratiti prenos predavanja na ovom linku:
https://miteam.mi.sanu.ac.rs/call/dpesCPawfHWm6LN3L/4omy3gZWp8F_Q4RjQSiJO9g-PWGPlbZs_TYO3M6m00K



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