In my XSLT-stylesheet I wanted to define a xmlns-prefix for that
  null-namespace,

The XML Namespaces rec does not allow a prefix to be used with
no-namespaace.

With XML Namespace 1.0 (which is the version used by almost all systems)
xmlns:my=""
is a syntax error.
With WXML Namespace 1.1 xmlns:my="" is allowed but it does not make
<my:foo/> refer to foo in no-namespace it unbinds the prefix my (if it
had already been bound) so making <my:foo/> an error.

So your requested result isn't conformant to the XML namespaces rec, and
XSLT won't generate it for you.

David

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