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Remembering W. H. Schikhof

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Abstract

W. H. Schikhof (1937–2014) is considered one of the founders of p-Adic Analysis and devoted his mathematical life to expand the frontiers of this area of knowledge. At the same time, he was a loyal friend and colleague, a concerned teacher and an affectionate family man. Many of us are thankful for the privilege of having been his friends and sharing his ideas. In this article we will shortly state some biographical facts. Then we will point out and discuss different areas in which his research was crucial. At the end we present a complete list of his books and published articles.

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References

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  47. W. H. Schikhof, “Minimal-Hausdorff p-adic locally convex spaces,” Ann. Math. Blaise Pascal 2, 259–266 (1995).

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  48. W. H. Schikhof, “A scalar field for which c0 has no Hahn-Banach property,” Ann. Math. Blaise Pascal 2, 267–273 (1995).

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  49. W. H. Schikhof, “A perfect duality between p-adic Banach spaces and compactoids,” Indag. Math. (N.S.) 6, 325–339 (1995).

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  50. C. Perez-Garcia and W. H. Schikhof, “Finite-dimensional subspaces of the p-adic space ℓ ∞,” Canad. Math. Bull. 38, 360–365 (1995).

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  51. J. Kakol, C. Perez-Garcia and W. H. Schikhof, “Cardinality and Mackey topologies of non-Archimedean Banach and Fréchet spaces,” Bull. Polish Acad. Sci. Math. 44, 131–141 (1996).

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  52. T. Kiyosawa and W. H. Schikhof, “Non-Archimedean Eberlein-Šmulian theory,” Int. J. Math. Math. Sci. 19, 637–642 (1996).

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  55. S. Oortwijn and W. H. Schikhof, “Locally convex modules over the unit disk,” Lecture Notes in Pure and Appl. Math. 192, 305–326 (M. Dekker, New York, 1997).

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  58. G. Christol, Z. Mebkhout and W. H. Schikhof, “An application of c-compactness,” Lecture Notes in Pure and Appl. Math. 207, 39–44 (M. Dekker, New York, 1999).

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  60. C. Perez-Garcia and W. H. Schikhof, “The p-Adic Banach-Dieudonné theorem and semi-compact inductive limits,” Lecture Notes in Pure and Appl. Math. 207, 295–307 (M. Dekker, New York, 1999).

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  61. W. H. Schikhof, “p-Adic convex functions,” p-Adic Analysis, Summability Theory, Fuzzy Analysis and Applications (Proc. of the International Conference Held in Honor of Prof. M. S. Rangachari and Prof. G. Rangan, Chennai, India, 1998), J. Anal. 7, 103–115 (1999).

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  62. W. H. Schikhof and H. Ochsenius, “Linear homeomorphisms of non-classical Hilbert spaces,” Indag. Math. (N.S.) 10, 601–613 (1999).

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  63. H. Ochsenius and W. H. Schikhof, “Hilbert-like spaces over valued fields,” Proc. of the First Math. Meeting in Memory of Herbert Gross (Locarno, Switzerland, 1999), Note di Matematica e Fisica 10, 31–51 (1999).

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  64. N. De Grande-De Kimpe, J. Kakol, C. Perez-Garcia and W. H. Schikhof, “Orthogonal sequences in non-Archimedean locally convex spaces,” Indag. Math. (N.S.) 11, 187–195 (2000).

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  65. W. H. Schikhof, “Banach spaces over non-Archimedean valued fields,” Topology Proc. 24, 547–581 (2001).

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  66. W. H. Schikhof, “An approach to the ultrametric moment problem,” Circumspice, Various papers in and Around Mathematics in Honor of Arnoud van Rooij, pp. 141–148 (Catholic Univ. of Nijmegen, The Netherlands, 2001).

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  67. N. DeGrande-DeB Kimpe, J. Kakol, C. Perez-Garcia and W. H. Schikhof, “Orthogonal and Schauder bases in non-Archimedean locally convex spaces,” Lecture Notes in Pure and Appl. Math. 222, 103–126 (M. Dekker, New York, 2001).

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  68. H. Keller, H. Ochsenius and W. H. Schikhof, “On the commutation relation AB − BA = I for operators on non-classical Hilbert spaces,” Lecture Notes in Pure and Appl. Math. 222, 177–190 (M. Dekker, New York, 2001).

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  69. H. Keller and W. H. Schikhof, “Probability measures on non-Archimedean inner product spaces,” Lecture Notes in Pure and Appl. Math. 222, 191–201 (M. Dekker, New York, 2001).

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  70. C. Perez-Garcia and W. H. Schikhof, “An approximation theorem for p-adic linear forms,” Lecture Notes in Pure and Appl. Math. 222, 255–260 (M. Dekker, New York, 2001).

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  71. W. H. Schikhof, “Towards a p-adic Müntz theorem,” Bull. Belg. Math. Soc. Simon Stevin 9, 169–185 (2002).

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  72. N. De Grande-De Kimpe, J. Kakol, C. Perez-Garcia and W. H. Schikhof, “Weak bases in p-adic spaces,” Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 5, 667–676 (2002).

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  73. H. Ochsenius and W. H. Schikhof, “Compact operators on non-classical Hilbert spaces,” Contemp. Math. 319, 239–249 (Amer. Math. Soc., Providence, RI, 2003).

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  74. C. Perez-Garcia and W. H. Schikhof, “Finite-dimensional orthocomplemented subspaces in p-adic normed spaces,” Contemp. Math. 319, 281–298 (Amer. Math. Soc., Providence, RI, 2003).

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  75. W. H. Schikhof, “An approach to the ultrametric moment problem,” Selected Topics of p-Adic Mathematical Physics and Analysis (Proc. of the First Conference on p-Adic Math. Physics,Moscow, Russia, 2003), Proc. Steklov Inst. Math. 245, 237–242 (2004).

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  76. H. Ochsenius and W. H. Schikhof, “Lipschitz operators on Banach spaces over Krull valued fields,” Contemp. Math. 384, 203–233 (Amer. Math. Soc., Providence, RI, 2005).

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  77. W. H. Schikhof, “p-Adic Choquet theory,” Contemp. Math. 384, 281–298 (Amer. Math. Soc., Providence, RI, 2005).

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  78. W. H. Schikhof, “Barrelledness of p-adic C1-function spaces,” p-Adic Mathematical Physics (Proc. of the Second Conference on p-Adic Math. Physics, Belgrade, Serbia, 2005), AIP Conf. Proc. 826, 280–290 (Amer. Inst. Phys., Melville, NY, 2006).

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  79. H. Ochsenius and W. H. Schikhof, “Norm Hilbert spaces over Krull valued fields,” Indag. Math. (N.S.) 17, 65–84 (2006).

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  80. H. Ochsenius and W. H. Schikhof, “Matrix characterizations of Lipschitz operators on Banach spaces over Krull valued fields,” Bull. Belg. Math. Soc. Simon Stevin 14, 193–212 (2007).

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  81. W. H. Schikhof, “Ultrametric C n-spaces of countable type,” Bull. Belg. Math. Soc. Simon Stevin 14, 993–1000 (2007).

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  82. H. Ochsenius and W. H. Schikhof, “On the algebraic dimension of Banach spaces over non-Archimedean valued fields of arbitrary rank,” Proyecciones 26, 237–244 (2007).

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  83. W.H. Schikhof, “An analyst encountering orthomodularity,” textit Proc. of the Second Mathematical Meeting in Memory of Herbert Gross, Note di Matematica e Fisica, Anno 22. 13, 3–12 (2009).

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  84. C. Perez-Garcia and W. H. Schikhof, Locally Convex Spaces Over non-Archimedean Valued Fields (Cambridge Univ. Press, Cambridge, 2010).

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  85. H. Ochsenius and W. H. Schikhof, “Compact perturbations of Fredholm operators on norm Hilbert spaces over Krull valued fields,” Contemp. Math. 508, 147–159 (Amer. Math. Soc., Providence, RI, 2010).

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  86. C. Perez-Garcia and W. H. Schikhof, “Tensor products of p-adic locally convex spaces having the strongest locally convex topology,” Contemp. Math. 508, 181–185 (Amer. Math. Soc., Providence, RI, 2010).

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  87. H. Ochsenius and W. H. Schikhof, “A new method for comparing two norm Hilbert spaces and their operators,” Indag. Math. (N.S.) 21, 112–126 (2011).

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  88. C. Perez-Garcia and W. H. Schikhof, “Remembering Nicole De Grande-De Kimpe 1936–2008,” Contemp. Math. 551, 1–32 (Amer. Math. Soc., Providence, RI, 2011).

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  91. E. Olivos and W. H. Schikhof, “Algebra and topology on the Dedekind completion of a totally ordered abelian group,” Indag. Math. (N.S.) 24, 291–304 (2013).

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  93. C. Perez-Garcia and W. H. Schikhof, “The metric approximation property in non-Archimedean normed spaces,” To be published in Glasnik Matematicki.

  94. W. H. Schikhof and E. Olivos, “A note on Banach spaces over a rank 1 discretely valued field,” To be published in Contemp. Math.

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  96. H. Ochsenius and E. Olivos, “On the value group and norms of a form Hilbert space,” Contemp. Math., 508, 133–146 (2010).

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  98. E. Olivos, H. Soto and A. Mansilla, “A characterization of the Dedekind completion of a totally ordered group of infinite rank,” Indag. Math. (N.S.) 19(4), 633–641 (2008).

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Authors and Affiliations

  1. Departamento de Matemática y Estadística, Facultad de Ingeniería y Ciencias Universidad de La Frontera, Temuco, Chile

    H. Ochsenius & E. Olivos

  2. Departamento de Matemáticas, Facultad de Ciencias Universidad de Cantabria, Avda. de los Castros s/n, 39071, Santander, Spain

    C. Perez-Garcia

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  1. H. Ochsenius
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  2. E. Olivos
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  3. C. Perez-Garcia
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Correspondence to H. Ochsenius.

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Ochsenius, H., Olivos, E. & Perez-Garcia, C. Remembering W. H. Schikhof. P-Adic Num Ultrametr Anal Appl 7, 81–95 (2015). https://doi.org/10.1134/S2070046615020016

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