BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//TYPO3/NONSGML Calendarize//EN
BEGIN:VEVENT
UID:calendarize-distances-between-operators-acting-on-different-hilbert-sp
 aces
DTSTAMP:20260703T095331Z
DTSTART:20260708T151500Z
SUMMARY:Distances between operators acting on different Hilbert spaces
DESCRIPTION:Vortragsankündigung\nIm Rahmen des Kolloquiums sprichtHerr Pr
 of. Dr. Olaf Post (Universität Trier)\nDistances between operators acting
  on different Hilbert spaces\nABSTRACTIn this talk we will define and comp
 are several distances (or metrics) between operators actingon different (s
 eparable) Hilbert spaces. We consider here three main cases of how to meas
 urethe distance between two bounded operators: first by taking the distanc
 e between their unitaryorbits\, second by isometric embeddings (this gener
 alises a concept of Weidmann) and third byquasi-unitary equivalence.Our ma
 in result is that the unitary and isometric distances are equal provided t
 he operators areboth self-adjoint and have 0 in their essential spectra. M
 oreover\, the quasi-unitary distance isequivalent (up to a universal const
 ant) with the isometric distance for any pair of boundedoperators. The uni
 tary distance gives an upper bound on the Hausdorff distance of theirspect
 rum. If both operators have purely essential spectrum\, then the unitary d
 istance equalsthe Hausdorff distance of their spectra. Using a finer spect
 ral distance respecting multiplicity ofdiscrete eigenvalues\, this spectra
 l distance equals the unitary distance also for operators withessential an
 d discrete spectrum. In particular\, all operator distances mentioned abov
 e areequal to this spectral distance resp. controlled by it in the quasi-u
 nitary case for self-adjointoperators with 0 in the essential spectrum. We
  also show that our results are sharp bypresenting various(counter-)exampl
 es (joint work with Sebastian Zimmer). \nDer Vortrag findet statt amMittw
 och\, den 08.07.2026um 17.15 Uhr im Raum W01 0-006Kaffee/Tee um 16.45 Uhr 
 im Raum W1 2-213\nInteressierte sind herzlich eingeladen. 
X-ALT-DESC;FMTTYPE=text/html:<h2 class="text-center"><strong>Vortragsankü
 ndigung</strong></h2>\n<h3 class="text-center"><br>Im Rahmen des Kolloquiu
 ms spricht<br><strong>Herr Prof. Dr. Olaf Post (Universität Trier)</stron
 g></h3>\n<h2 class="text-center"><br><strong>Distances between operators a
 cting on different Hilbert spaces</strong></h2>\n<p class="text-center"><b
 r />ABSTRACT<br />In this talk we will define and compare several distance
 s (or metrics) between operators acting<br />on different (separable) Hilb
 ert spaces. We consider here three main cases of how to measure<br />the d
 istance between two bounded operators: first by taking the distance betwee
 n their unitary<br />orbits\, second by isometric embeddings (this general
 ises a concept of Weidmann) and third by<br />quasi-unitary equivalence.<b
 r />Our main result is that the unitary and isometric distances are equal 
 provided the operators are<br />both self-adjoint and have 0 in their esse
 ntial spectra. Moreover\, the quasi-unitary distance is<br />equivalent (u
 p to a universal constant) with the isometric distance for any pair of bou
 nded<br />operators. The unitary distance gives an upper bound on the Haus
 dorff distance of their<br />spectrum. If both operators have purely essen
 tial spectrum\, then the unitary distance equals<br />the Hausdorff distan
 ce of their spectra. Using a finer spectral distance respecting multiplici
 ty of<br />discrete eigenvalues\, this spectral distance equals the unitar
 y distance also for operators with<br />essential and discrete spectrum. I
 n particular\, all operator distances mentioned above are<br />equal to th
 is spectral distance resp. controlled by it in the quasi-unitary case for 
 self-adjoint<br />operators with 0 in the essential spectrum. We also show
  that our results are sharp by<br />presenting various(counter-)examples (
 joint work with Sebastian Zimmer).<br />&nbsp\;</p>\n<p class="text-center
 "><strong>Der Vortrag findet statt am<br />Mittwoch\, den 08.07.2026<br />
 um 17.15 Uhr im Raum W01 0-006<br />Kaffee/Tee um 16.45 Uhr im Raum W1 2-2
 13</strong></p>\n<p class="text-center"><br />Interessierte sind herzlich 
 eingeladen.<br />&nbsp\;</p>
LOCATION:
END:VEVENT
END:VCALENDAR