Superstability for Generalized Module Left Derivations and Generalized Module Derivations on a Banach Module (I)
We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let 𝒜 be a Banach algebra and X a Banach 𝒜-module, f:X→X and g:𝒜→𝒜. The mappings Δf,g1,&#x...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/718020 |
| Summary: | We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let 𝒜 be a Banach algebra and X a Banach 𝒜-module, f:X→X and g:𝒜→𝒜. The mappings Δf,g1, Δf,g2, Δf,g3, and Δf,g4 are defined and it is proved that if ∥Δf,g1(x,y,z,w)∥ (resp., ∥Δf,g3(x,y,z,w,α,β)∥) is dominated by φ(x,y,z,w), then f is a generalized (resp., linear) module-𝒜 left derivation and g is a (resp., linear) module-X left derivation. It is also shown that if ∥Δf,g2(x,y,z,w)∥ (resp., ∥Δf,g4(x,y,z,w,α,β)∥) is dominated by φ(x,y,z,w), then f is a generalized (resp., linear) module-𝒜 derivation and g is a (resp., linear) module-X derivation. |
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| ISSN: | 1025-5834 1029-242X |