Geodesic
Ideal $F$-norms on $C^*$-algebras
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 69-74

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We show that every noncompactness measure on a $W^*$-algebra is an ideal $F$-pseudonorm. We establish the criterion of right Fredholm property of an element with respect to $W^*$-algebra. We prove that the element $-I$ realizes maximum distance from the positive element to the subset of all isometries of unital $C^*$-algebra, here $I$ is the unit of $C^*$-algebra. We also consider differences of two finite products of elements from the unit ball of $C^*$-algebra and obtain an estimate of their ideal $F$-pseudonorms. The paper is concluded with the convergence criterion in complete ideal $F$-norm for two series of elements from $W^*$-algebra.
Keywords: $C^*$-algebra, $W^*$-algebra, trace, Hilbert space, linear operator, Fredholm operator, isometry, unitary operator, compact operator, ideal, ideal $F$-norm, measure of noncompactness. 
@article{IVM_2015_5_a7,
     author = {A. M. Bikchentaev},
     title = {Ideal $F$-norms on $C^*$-algebras},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {69--74},
     publisher = {mathdoc},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_5_a7/}
}
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A. M. Bikchentaev. Ideal $F$-norms on $C^*$-algebras. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2015), pp. 69-74. http://geodesic.mathdoc.fr/item/IVM_2015_5_a7/