<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">M. Anoussis, G. K. Eleftherakis, A. Katavolos</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Synthetic properties of locally compact groups: preservation and transference</style></title><secondary-title><style face="normal" font="default" size="100%"> Monatshefte für Mathematik</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2023</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s00605-022-01736-8</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">201</style></volume><pages><style face="normal" font="default" size="100%">329-347</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Using techniques from TRO equivalence of masa bimodules we prove various transference results: We show that when &lt;span id=&quot;MathJax-Element-1-Frame&quot; class=&quot;MathJax&quot;&gt;&lt;span id=&quot;MathJax-Span-1&quot; style=&quot;width: 0.745em; display: inline-block;&quot; class=&quot;math&quot;&gt;&lt;span style=&quot;display: inline-block; position: relative; width: 0.618em; height: 0px; font-size: 119%;&quot;&gt;&lt;span style=&quot;position: absolute; clip: rect(1.535em, 1000.58em, 2.359em, -1000em); top: -2.163em; left: 0em;&quot;&gt;&lt;span id=&quot;MathJax-Span-2&quot; class=&quot;mrow&quot;&gt;&lt;span id=&quot;MathJax-Span-3&quot; style=&quot;font-family: MathJax_Math; font-style: italic;&quot; class=&quot;mi&quot;&gt;α&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;display: inline-block; width: 0px; height: 2.163em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;display: inline-block; overflow: hidden; vertical-align: -0.087em; border-left: 0px solid; width: 0px; height: 0.686em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; is a group homomorphism which pushes forward the Haar measure of G to a measure absolutely continuous with respect to the Haar measure on H, then &lt;span id=&quot;MathJax-Element-4-Frame&quot; class=&quot;MathJax&quot;&gt;&lt;span id=&quot;MathJax-Span-10&quot; style=&quot;width: 5.07em; display: inline-block;&quot; class=&quot;math&quot;&gt;&lt;span style=&quot;display: inline-block; position: relative; width: 4.263em; height: 0px; font-size: 119%;&quot;&gt;&lt;span style=&quot;position: absolute; clip: rect(1.267em, 1004.26em, 2.722em, -1000em); top: -2.286em; left: 0em;&quot;&gt;&lt;span id=&quot;MathJax-Span-11&quot; class=&quot;mrow&quot;&gt;&lt;span id=&quot;MathJax-Span-12&quot; style=&quot;font-family: MathJax_Main;&quot; class=&quot;mo&quot;&gt;(&lt;/span&gt;&lt;span id=&quot;MathJax-Span-13&quot; style=&quot;font-family: MathJax_Math; font-style: italic;&quot; class=&quot;mi&quot;&gt;α&lt;/span&gt;&lt;span id=&quot;MathJax-Span-14&quot; style=&quot;font-family: MathJax_Main; padding-left: 0.222em;&quot; class=&quot;mo&quot;&gt;×&lt;/span&gt;&lt;span id=&quot;MathJax-Span-15&quot; style=&quot;font-family: MathJax_Math; font-style: italic; padding-left: 0.222em;&quot; class=&quot;mi&quot;&gt;α&lt;/span&gt;&lt;span id=&quot;MathJax-Span-16&quot; class=&quot;msubsup&quot;&gt;&lt;span style=&quot;display: inline-block; position: relative; width: 1.368em; height: 0px;&quot;&gt;&lt;span style=&quot;position: absolute; clip: rect(3.081em, 1000.29em, 4.452em, -1000em); top: -4.016em; left: 0em;&quot;&gt;&lt;span id=&quot;MathJax-Span-17&quot; style=&quot;font-family: MathJax_Main;&quot; class=&quot;mo&quot;&gt;)&lt;/span&gt;&lt;span style=&quot;display: inline-block; width: 0px; height: 4.016em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;position: absolute; top: -4.379em; left: 0.389em;&quot;&gt;&lt;span id=&quot;MathJax-Span-18&quot; class=&quot;texatom&quot;&gt;&lt;span id=&quot;MathJax-Span-19&quot; class=&quot;mrow&quot;&gt;&lt;span id=&quot;MathJax-Span-20&quot; style=&quot;font-size: 70.7%; font-family: MathJax_Main;&quot; class=&quot;mo&quot;&gt;−&lt;/span&gt;&lt;span id=&quot;MathJax-Span-21&quot; style=&quot;font-size: 70.7%; font-family: MathJax_Main;&quot; class=&quot;mn&quot;&gt;1&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;display: inline-block; width: 0px; height: 4.016em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;display: inline-block; width: 0px; height: 2.286em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;display: inline-block; overflow: hidden; vertical-align: -0.371em; border-left: 0px solid; width: 0px; height: 1.437em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; preserves sets of compact operator synthesis, and conversely when &lt;span id=&quot;MathJax-Element-5-Frame&quot; class=&quot;MathJax&quot;&gt;&lt;span id=&quot;MathJax-Span-22&quot; style=&quot;width: 0.745em; display: inline-block;&quot; class=&quot;math&quot;&gt;&lt;span style=&quot;display: inline-block; position: relative; width: 0.618em; height: 0px; font-size: 119%;&quot;&gt;&lt;span style=&quot;position: absolute; clip: rect(1.535em, 1000.58em, 2.359em, -1000em); top: -2.163em; left: 0em;&quot;&gt;&lt;span id=&quot;MathJax-Span-23&quot; class=&quot;mrow&quot;&gt;&lt;span id=&quot;MathJax-Span-24&quot; style=&quot;font-family: MathJax_Math; font-style: italic;&quot; class=&quot;mi&quot;&gt;α&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;display: inline-block; width: 0px; height: 2.163em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span style=&quot;display: inline-block; overflow: hidden; vertical-align: -0.087em; border-left: 0px solid; width: 0px; height: 0.686em;&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt; is onto. We also prove similar preservation results for operator Ditkin sets and operator M-sets, obtaining preservation results for M-sets as corollaries. Some of these results extend or complement existing results of Ludwig, Shulman, Todorov and Turowska.</style></abstract></record></records></xml>