59,702 research outputs found
On the continuity and differentiability of the (dual) core inverse in C*-algebras
[EN] The continuity of the core inverse and the dual core inverse is studied in the setting of -algebras. Later, this study is specialized to the case of bounded Hilbert space operators and to complex matrices. In addition, the differentiability of these generalized inverses is studied in the context of -algebras.The third author is supported by the Scientific Research Foundation for doctorate programme at Huaiyin Institute of Technology [grant number Z301B18534]. The third author is grateful to China Scholarship Council for helping him pursue his further study at Universitat PolitĂšcnica de ValĂšncia, SpainBenĂtez LĂłpez, J.; Boasso, E.; Xu, S. (2020). On the continuity and differentiability of the (dual) core inverse in C*-algebras. Linear and Multilinear Algebra. 68(4):686-709. https://doi.org/10.1080/03081087.2018.1516187S686709684Baksalary, O. M., & Trenkler, G. (2010). Core inverse of matrices. Linear and Multilinear Algebra, 58(6), 681-697. doi:10.1080/03081080902778222RakiÄ, D. S., DinÄiÄ, N. Ä., & DjordjeviÄ, D. S. (2014). Group, MooreâPenrose, core and dual core inverse in rings with involution. Linear Algebra and its Applications, 463, 115-133. doi:10.1016/j.laa.2014.09.003RakiÄ, D. S., DinÄiÄ, N. Ä., & DjordjeviÄ, D. S. (2014). Core inverse and core partial order of Hilbert space operators. Applied Mathematics and Computation, 244, 283-302. doi:10.1016/j.amc.2014.06.112Xu, S., Chen, J., & Zhang, X. (2016). New characterizations for core inverses in rings with involution. Frontiers of Mathematics in China, 12(1), 231-246. doi:10.1007/s11464-016-0591-2Drazin, M. P. (2012). A class of outer generalized inverses. Linear Algebra and its Applications, 436(7), 1909-1923. doi:10.1016/j.laa.2011.09.004Boasso, E., & KantĂșn-Montiel, G. (2017). The (b, c)-Inverse in Rings and in the Banach Context. Mediterranean Journal of Mathematics, 14(3). doi:10.1007/s00009-017-0910-1Harte, R. (1992). On generalized inverses in C*-algebras. Studia Mathematica, 103(1), 71-77. doi:10.4064/sm-103-1-71-77Harte, R. (1993). Generalized inverses in C*-algebras II. Studia Mathematica, 106(2), 129-138. doi:10.4064/sm-106-2-129-138Penrose, R. (1955). A generalized inverse for matrices. Mathematical Proceedings of the Cambridge Philosophical Society, 51(3), 406-413. doi:10.1017/s0305004100030401Mbekhta, M. (1992). Conorme et Inverse GĂ©nĂ©ralisĂ© Dans Les C*-AlgĂšbres. Canadian Mathematical Bulletin, 35(4), 515-522. doi:10.4153/cmb-1992-068-8Du, F., & Xue, Y. (2012). Perturbation analysis of A_{T,S}^(2) on Banach Spaces. The Electronic Journal of Linear Algebra, 23. doi:10.13001/1081-3810.1543BenĂtez, J., CvetkoviÄ-IliÄ, D., & Liu, X. (2014). On the continuity of the group inverse in -algebras. Banach Journal of Mathematical Analysis, 8(2), 204-213. doi:10.15352/bjma/1396640064BenĂtez, J., & CvetkoviÄ-IliÄ, D. (2013). On the elements aaâ and aâ a in a ring. Applied Mathematics and Computation, 222, 478-489. doi:10.1016/j.amc.2013.07.015Koliha, J. J. (2001). Continuity and differentiability of the Moore-Penrose inverse in -algebras. MATHEMATICA SCANDINAVICA, 88(1), 154. doi:10.7146/math.scand.a-14320Koliha, J. J., & RakoÄeviÄ, V. (2004). On the Norm of Idempotents in -Algebras. Rocky Mountain Journal of Mathematics, 34(2). doi:10.1216/rmjm/1181069874BenĂtez, J., & Liu, X. (2012). On the continuity of the group inverse. Operators and Matrices, (4), 859-868. doi:10.7153/oam-06-55Douglas, R. G. (1966). On majorization, factorization, and range inclusion of operators on Hilbert space. Proceedings of the American Mathematical Society, 17(2), 413-413. doi:10.1090/s0002-9939-1966-0203464-1Boasso, E. (2009). Drazin spectra of Banach space operators and Banach algebra elements. Journal of Mathematical Analysis and Applications, 359(1), 48-55. doi:10.1016/j.jmaa.2009.05.036RakiÄ, D. S. (2017). A note on Rao and Mitraâs constrained inverse and Drazinâs (b,c) inverse. Linear Algebra and its Applications, 523, 102-108. doi:10.1016/j.laa.2017.02.025Stewart, G. W. (1969). On the Continuity of the Generalized Inverse. SIAM Journal on Applied Mathematics, 17(1), 33-45. doi:10.1137/011700
Generalized backscattering and the Lax-Phillips transform
Using the free-space translation representation (modified Radon transform) of
Lax and Phillips in odd dimensions, it is shown that the generalized
backscattering transform (so outgoing angle in terms of the
incoming angle with orthogonal and \Id-S invertible) may be further
restricted to give an entire, globally Fredholm, operator on appropriate
Sobolev spaces of potentials with compact support. As a corollary we show that
the modified backscattering map is a local isomorphism near elements of a
generic set of potentials.Comment: Minor changes, typos corrected, references adde
Generalized quantum potentials in scale relativity
We first recall that the system of fluid mechanics equations (Euler and
continuity) that describes a fluid in irrotational motion subjected to a
generalized quantum potential (in which the constant is no longer reduced to
the standard quantum constant hbar) is equivalent to a generalized Schrodinger
equation. Then we show that, even in the case of the presence of vorticity, it
is also possible to obtain, for a large class of systems, a Schrodinger-like
equation of the vectorial field type from the continuity and Euler equations
including a quantum potential. The same kind of transformation also applies to
a classical charged fluid subjected to an electromagnetic field and to an
additional potential having the form of a quantum potential. Such a fluid can
therefore be described by an equation of the Ginzburg-Landau type, and is
expected to show some superconducting-like properties. Moreover, a Schrodinger
form can be obtained for the fluctuating rotational motion of a solid. In this
case the mass is replaced by the tensor of inertia, and a generalized form of
the quantum potential is derived. We finally reconsider the case of a standard
diffusion process, and we show that, after a change of variable, the diffusion
equation can also be given the form of a continuity and Euler system including
an additional potential energy. Since this potential is exactly the opposite of
a quantum potential, the quantum behavior may be considered, in this context,
as an anti-diffusion.Comment: 33 pages, submitted for publicatio
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