Spectral properties of certain operators on the free Hilbert space ℑ [H1, . . . , HN] and the semicircular law

• Autorzy: Cho Ilwoo

Identyfikatory

DOI

10.7494/OpMath.2021.41.6.755

• Języki publikacji: EN

Abstrakty

EN

In this paper, we fix N -many l2-Hilbert spaces Hk whose dimensions are [formula] for k=1,…, N, for N ∈N\{1}. And then, construct a Hilbert space ℑ = ℑ [H1 , . . . , HN] induced by H1 , . . . , HN, and study certain types of operators on ℑ. In particular, we are interested in so-called jump-shift operators. The main results (i) characterize the spectral properties of these operators, and (ii) show how such operators affect the semicircular law induced by [formula], where Bk are the orthonormal bases of Hk , for k = 1, . . . , N.

Słowa kluczowe

EN

separable Hilbert spaces; free Hilbert spaces; jump operator; shift operators; jump-shift operators; semicircular elements

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 6
• Strony: 755--803
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Cho Ilwoo

• St. Ambrose University Department of Mathematics and Statistics 518 W. Locust St., Davenport, Iowa, 52803, U.S.A.

Bibliografia

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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).