Putnam-Fuglede theorem and the range-kernel orthogonality of derivations
Let ℬ(H) denote the algebra of operators on a Hilbert space H into itself. Let d=δ or Δ, where δAB:ℬ(H)→ℬ(H) is the generalized derivation δAB(S)=AS−SB and ΔAB:ℬ(H)→ℬ(H) is the elementary operator ΔAB(S)=ASB−S. Given A,B,S∈ℬ(H), we say that the pair (A,B) has the property PF(d(S)) if dAB(S)=0 implie...
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| Format: | Article |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201006159 |
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| _version_ | 1832561788240003072 |
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| author | B. P. Duggal |
| author_facet | B. P. Duggal |
| author_sort | B. P. Duggal |
| collection | DOAJ |
| description | Let ℬ(H) denote the algebra of operators on a Hilbert
space H into itself. Let d=δ or Δ, where δAB:ℬ(H)→ℬ(H) is the generalized derivation δAB(S)=AS−SB and ΔAB:ℬ(H)→ℬ(H) is the elementary operator ΔAB(S)=ASB−S. Given A,B,S∈ℬ(H), we say that the pair (A,B) has the property PF(d(S)) if dAB(S)=0 implies dA∗B∗(S)=0. This paper characterizes operators A,B, and S for which the pair (A,B) has property PF(d(S)), and establishes a relationship between the PF(d(S))-property of the pair (A,B) and the range-kernel orthogonality of the operator dAB. |
| format | Article |
| id | doaj-art-ae150c8755304558bdf7042331d9f1e1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ae150c8755304558bdf7042331d9f1e12025-02-03T01:24:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0127957358210.1155/S0161171201006159Putnam-Fuglede theorem and the range-kernel orthogonality of derivationsB. P. Duggal0Department of Mathematics, Faculty of Science, United Arab Emirates University, P.O. Box 17551, Al Ain, United Arab EmiratesLet ℬ(H) denote the algebra of operators on a Hilbert space H into itself. Let d=δ or Δ, where δAB:ℬ(H)→ℬ(H) is the generalized derivation δAB(S)=AS−SB and ΔAB:ℬ(H)→ℬ(H) is the elementary operator ΔAB(S)=ASB−S. Given A,B,S∈ℬ(H), we say that the pair (A,B) has the property PF(d(S)) if dAB(S)=0 implies dA∗B∗(S)=0. This paper characterizes operators A,B, and S for which the pair (A,B) has property PF(d(S)), and establishes a relationship between the PF(d(S))-property of the pair (A,B) and the range-kernel orthogonality of the operator dAB.http://dx.doi.org/10.1155/S0161171201006159 |
| spellingShingle | B. P. Duggal Putnam-Fuglede theorem and the range-kernel orthogonality of derivations International Journal of Mathematics and Mathematical Sciences |
| title | Putnam-Fuglede theorem and the range-kernel orthogonality of derivations |
| title_full | Putnam-Fuglede theorem and the range-kernel orthogonality of derivations |
| title_fullStr | Putnam-Fuglede theorem and the range-kernel orthogonality of derivations |
| title_full_unstemmed | Putnam-Fuglede theorem and the range-kernel orthogonality of derivations |
| title_short | Putnam-Fuglede theorem and the range-kernel orthogonality of derivations |
| title_sort | putnam fuglede theorem and the range kernel orthogonality of derivations |
| url | http://dx.doi.org/10.1155/S0161171201006159 |
| work_keys_str_mv | AT bpduggal putnamfugledetheoremandtherangekernelorthogonalityofderivations |