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EspañolPOSITIVE_ELEMENT
(Redirected from Positive operator)
In mathematics, especially functional analysis, a hermitian element ''A'' of a C
★ -algebra is a 'positive element' if its spectrum consists of positive real numbers. Equivalently, ''A'' has a hermitian square root, that is an element ''B'' of the C
★ -algebra satisfying ''B
★ =B'' and ''B''2=''A''.
If ''A'' is a bounded linear operator on a Hilbert space ''H'', then this notion coincides with the condition that
:
be positive for every vector ''x'' in ''H''.
In mathematics, especially functional analysis, a hermitian element ''A'' of a C
★ -algebra is a 'positive element' if its spectrum consists of positive real numbers. Equivalently, ''A'' has a hermitian square root, that is an element ''B'' of the C
★ -algebra satisfying ''B
★ =B'' and ''B''2=''A''.
If ''A'' is a bounded linear operator on a Hilbert space ''H'', then this notion coincides with the condition that
:
be positive for every vector ''x'' in ''H''.
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