{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:V3LGK4VOP5WPNFVXIELWJKQ7KW","short_pith_number":"pith:V3LGK4VO","schema_version":"1.0","canonical_sha256":"aed66572ae7f6cf696b7411764aa1f5584bba9a9dee88c634dbcec1bbc65a67b","source":{"kind":"arxiv","id":"1006.1941","version":1},"attestation_state":"computed","paper":{"title":"Dunkl--Williams inequality for operators \\\\ associated with $p$-angular distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"F. Dadipour, M. Fujii, M. S. Moslehian","submitted_at":"2010-06-10T02:42:07Z","abstract_excerpt":"We present several operator versions of the Dunkl--Williams inequality with respect to the $p$-angular distance for operators. More precisely, we show that if $A, B \\in \\mathbb{B}(\\mathscr{H})$ such that $|A|$ and $|B|$ are invertible, $\\frac{1}{r}+\\frac{1}{s}=1\\,\\,(r>1)$ and $p\\in\\mathbb{R}$, then \\begin{equation*} |A|A|^{p-1}-B|B|^{p-1}|^{2} \\leq |A|^{p-1}(r|A-B|^{2}+s||A|^{1-p}|B|^{p}-|B||^2)|A|^{p-1}.%\\nonumber \\end{equation*} In the case that $0

1)$ and $p\\in\\mathbb{R}$, then \\begin{equation*} |A|A|^{p-1}-B|B|^{p-1}|^{2} \\leq |A|^{p-1}(r|A-B|^{2}+s||A|^{1-p}|B|^{p}-|B||^2)|A|^{p-1}.%\\nonumber \\end{equation*} In the case that $0