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SUMMARY:Distances between operators acting on different Hilbert spaces
DESCRIPTION:Lecture announcement\nAs part of the colloquium\,Prof. Dr Olaf
  Post (University of Trier) will givea\nDistances between operators acting
  on different Hilbert spaces\nABSTRACTIn this talk\, we will define and co
 mpare several distances (or metrics) between operators actingon different 
 (separable) Hilbert spaces. We consider here three main cases for measurin
 g the distance between two bounded operators: first\, by taking the distan
 ce between their unitary--orbits\; second\, by isometric embeddings (this 
 generalises a concept introduced by Weidmann)\; and third\, by quasi-unita
 ry equivalence.Our main result is that the unitary and isometric distances
  are equal provided the operators are\, both self-adjoint and have 0 in th
 eir essential spectra. Moreover\, the quasi-unitary distance is-equivalent
  (up to a universal constant) to the isometric distance for any pair of bo
 undedoperators. The unitary distance provides an upper bound on the Hausdo
 rff distance of theirspectrum. If both operators have a purely essential s
 pectrum\, then the unitary distance equalsthe Hausdorff distance of their 
 spectra. Using a finer spectral distance that takes into account the multi
 plicity ofdiscrete eigenvalues\, this spectral distance also equals the un
 itary distance for operators withessential and discrete spectrum. In parti
 cular\, all the operator distances mentioned above areequal to this spectr
 al distance\, or controlled by it\, in the quasi-unitary case for self-adj
 ointoperators with 0 in the essential spectrum. We also show that our resu
 lts are sharp bypresenting various (counter-)examples (joint work with Seb
 astian Zimmer). \nThe lecture will take place onWednesday\, 8 July 2026at 
 5.15 pm in room W01 0-006Coffee/tea at 4.45 pm in room W1 2-213\nAnyone in
 terested is warmly invited. 
X-ALT-DESC;FMTTYPE=text/html:<h2 class="text-center"><strong>Lecture annou
 ncement</strong></h2>\n<h3 class="text-center"><br>As part of the colloqui
 um\,<strong>Prof. Dr Olaf Post (University of Trier)</strong> will give<st
 rong>a</strong><br><strong></strong></h3>\n<h2 class="text-center"><br><st
 rong>Distances between operators acting on different Hilbert spaces</stron
 g></h2>\n<p class="text-center"><br />ABSTRACT<br />In this talk\, we will
  define and compare several distances (or metrics) between operators actin
 g<br />on different (separable) Hilbert spaces. We consider here three mai
 n cases for measuring the distance between two bounded operators<br />: fi
 rst\, by taking the distance between their unitary-<br />-orbits\; second\
 , by isometric embeddings (this generalises a concept introduced by Weidma
 nn)\; and third\, by quasi-unitary equivalence<br />.<br />Our main result
  is that the unitary and isometric distances are equal provided the operat
 ors are<br />\, both self-adjoint and have 0 in their essential spectra. M
 oreover\, the quasi-unitary distance is<br />-equivalent (up to a universa
 l constant) to the isometric distance for any pair of bounded<br />operato
 rs. The unitary distance provides an upper bound on the Hausdorff distance
  of their<br />spectrum. If both operators have a purely essential spectru
 m\, then the unitary distance equals<br />the Hausdorff distance of their 
 spectra. Using a finer spectral distance that takes into account the multi
 plicity of<br />discrete eigenvalues\, this spectral distance also equals 
 the unitary distance for operators with<br />essential and discrete spectr
 um. In particular\, all the operator distances mentioned above are<br />eq
 ual to this spectral distance\, or 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 /> </p>\n<p class="text-c
 enter"><strong>The lecture will take place on<br />Wednesday\, 8 July 2026
 <br />at 5.15 pm in room W01 0-006<br />Coffee/tea at 4.45 pm in room W1 2
 -213</strong></p>\n<p class="text-center"><br />Anyone interested is warml
 y invited.<br /> </p>
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