Qaisar Latif - Academia.edu (original) (raw)

Papers by Qaisar Latif

Research paper thumbnail of Banach spaces without approximation properties of type p

Mathematical Notes, 2010

The main purpose of this note is to show that the question posed in the paper [1] of D. P. Sinha ... more The main purpose of this note is to show that the question posed in the paper [1] of D. P. Sinha D. P. and A. K. Karn (see the very end of that paper) has a negative answer, and that the answer could have been obtained, essentially, in 1985 after the papers [2], [3] by the author appeared in 1982 and 1985, respectively.

Research paper thumbnail of Grothendieck-Lidskii theorem for subspaces and factor spaces of L_p-spaces

In 1955, A. Grothendieck has shown that if the linear operator T in a Banach subspace of an L ∞ -... more In 1955, A. Grothendieck has shown that if the linear operator T in a Banach subspace of an L ∞ -space is 2/3-nuclear then the trace of T is well defined and is equal to the sum of all eigenvalues {µ k (T )} of T. V.B. Lidskiǐ , in 1959, proved his famous theorem on the coincidence of the trace of the S 1 -operator in L 2 (ν) with its spectral trace ∞ k=1 µ k (T ). We show that for p ∈ [1, ∞] and s ∈ (0, 1] with 1/s = 1 + |1/2 − 1/p|, and for every s-nuclear operator T in every subspace of any L p (ν)-space the trace of T is well defined and equals the sum of all eigenvalues of T. Note that for p = 2 one has s = 1, and for p = ∞ one has s = 2/3.

Research paper thumbnail of Advertisement for Online Applications 25 08 2013

Ph.D. from HEC recognized university/institution (OR) 1 st Class Master's degree or equivalent fr... more Ph.D. from HEC recognized university/institution (OR) 1 st Class Master's degree or equivalent from HEC recognized University / Institution with no 3rd division in the academic career. At least 5 years post qualification experience (OR) 10 years post qualification experience in case of Masters, in a University environment in teaching/research/ administration. Strong interpersonal and communication skills are required. Must have excellent command over spoken and written English. IT Proficiency is a must. ASSISTANT REGISTRAR: [KARACHI, LAHORE & MULTAN] Pay Scale: J-III Qualifications & Experience: Master's degree or equivalent (at least 2nd division) from HEC recognized University / Institution. At least 3 years post-qualification experience in office administration in a University/educational institution. IT proficiency is a must. CONTROLLER OF EXAMINATIONS' OFFICE ASSISTANT CONTROLLER EXAMINATIONS: [LAHORE] Pay Scale: J-III Qualifications & Experience: Four (4) Years BS degree in Computer Science/IT or equivalent (1st division) from HEC recognized University / Institution with no 3rd division in the academic career. SOFTWARE ENGINEER [LAHORE] Pay Scale: J-II Qualifications & Experience: 4-Year BS degree in Computer Science/IT or equivalent (1st division) from HEC recognized University / Institution. At least 2 Years post qualification experience of designing, developing and deploying complex software systems. Fluency in spoken and written English is required. Good domain knowledge of Learning and Content Management Systems as well as current programming tools and languages is a must. Experience of developing desktop and Internet based applications with strong database management skills is required. Excellent interpersonal skills will be an asset. JUNIOR WEBMASTER [LAHORE] Pay Scale: J-III Qualifications & Experience: 4-Year BS degree in Computer Science/IT or equivalent (1st division) from HEC recognized University / Institution. Excellent English writing and communication skills are mandatory. Should have experience with a wide variety of operating systems including Linux. Knowledge of configuring web-servers such as IIS, Apache etc. and proficiency in current web-development languages and tools is required. NETWORKING NETWORK EXECUTIVE [LAHORE] Pay Scale: E-III Qualifications & Experience: 1st Class 4-year BS(CS/IT) OR BE(EE) or equivalent from HEC recognized University/Institute with Network certification. At least 7 Years post qualification experience of designing, implementing and maintaining complex networks; capability to handle firewalls, routers, switches and other LAN/WAN equipment. Proficiency in installing, configuring and troubleshooting web, file, mail, DBMS, DNS and proxy servers etc. under Windows/Linux environments is required. Excellent command over spoken and written English. NETWORK MANAGER [KARACHI] Pay Scale: J-I Qualifications & Experience: 1st Class 4-year BS(CS/IT) OR BE(EE) or equivalent from HEC recognized University/Institute with Network certification. At least 3 Years post qualification experience of designing, implementing and maintaining complex networks; capability to handle firewalls, routers, switches and other LAN/WAN equipment. Proficiency in installing, configuring and troubleshooting web, file, mail, DBMS, DNS and proxy servers etc. under Windows/Linux environments is required. Excellent command over spoken and written English. NETWORK ADMINISTRATOR [ABBOTTABAD,

Research paper thumbnail of Banach spaces without approximation properties of type p

Mathematical Notes, 2010

The main purpose of this note is to show that the question posed in the paper [1] of D. P. Sinha ... more The main purpose of this note is to show that the question posed in the paper [1] of D. P. Sinha D. P. and A. K. Karn (see the very end of that paper) has a negative answer, and that the answer could have been obtained, essentially, in 1985 after the papers [2], [3] by the author appeared in 1982 and 1985, respectively.

Research paper thumbnail of Grothendieck-Lidskii theorem for subspaces and factor spaces of L_p-spaces

In 1955, A. Grothendieck has shown that if the linear operator T in a Banach subspace of an L ∞ -... more In 1955, A. Grothendieck has shown that if the linear operator T in a Banach subspace of an L ∞ -space is 2/3-nuclear then the trace of T is well defined and is equal to the sum of all eigenvalues {µ k (T )} of T. V.B. Lidskiǐ , in 1959, proved his famous theorem on the coincidence of the trace of the S 1 -operator in L 2 (ν) with its spectral trace ∞ k=1 µ k (T ). We show that for p ∈ [1, ∞] and s ∈ (0, 1] with 1/s = 1 + |1/2 − 1/p|, and for every s-nuclear operator T in every subspace of any L p (ν)-space the trace of T is well defined and equals the sum of all eigenvalues of T. Note that for p = 2 one has s = 1, and for p = ∞ one has s = 2/3.

Research paper thumbnail of Advertisement for Online Applications 25 08 2013

Ph.D. from HEC recognized university/institution (OR) 1 st Class Master's degree or equivalent fr... more Ph.D. from HEC recognized university/institution (OR) 1 st Class Master's degree or equivalent from HEC recognized University / Institution with no 3rd division in the academic career. At least 5 years post qualification experience (OR) 10 years post qualification experience in case of Masters, in a University environment in teaching/research/ administration. Strong interpersonal and communication skills are required. Must have excellent command over spoken and written English. IT Proficiency is a must. ASSISTANT REGISTRAR: [KARACHI, LAHORE & MULTAN] Pay Scale: J-III Qualifications & Experience: Master's degree or equivalent (at least 2nd division) from HEC recognized University / Institution. At least 3 years post-qualification experience in office administration in a University/educational institution. IT proficiency is a must. CONTROLLER OF EXAMINATIONS' OFFICE ASSISTANT CONTROLLER EXAMINATIONS: [LAHORE] Pay Scale: J-III Qualifications & Experience: Four (4) Years BS degree in Computer Science/IT or equivalent (1st division) from HEC recognized University / Institution with no 3rd division in the academic career. SOFTWARE ENGINEER [LAHORE] Pay Scale: J-II Qualifications & Experience: 4-Year BS degree in Computer Science/IT or equivalent (1st division) from HEC recognized University / Institution. At least 2 Years post qualification experience of designing, developing and deploying complex software systems. Fluency in spoken and written English is required. Good domain knowledge of Learning and Content Management Systems as well as current programming tools and languages is a must. Experience of developing desktop and Internet based applications with strong database management skills is required. Excellent interpersonal skills will be an asset. JUNIOR WEBMASTER [LAHORE] Pay Scale: J-III Qualifications & Experience: 4-Year BS degree in Computer Science/IT or equivalent (1st division) from HEC recognized University / Institution. Excellent English writing and communication skills are mandatory. Should have experience with a wide variety of operating systems including Linux. Knowledge of configuring web-servers such as IIS, Apache etc. and proficiency in current web-development languages and tools is required. NETWORKING NETWORK EXECUTIVE [LAHORE] Pay Scale: E-III Qualifications & Experience: 1st Class 4-year BS(CS/IT) OR BE(EE) or equivalent from HEC recognized University/Institute with Network certification. At least 7 Years post qualification experience of designing, implementing and maintaining complex networks; capability to handle firewalls, routers, switches and other LAN/WAN equipment. Proficiency in installing, configuring and troubleshooting web, file, mail, DBMS, DNS and proxy servers etc. under Windows/Linux environments is required. Excellent command over spoken and written English. NETWORK MANAGER [KARACHI] Pay Scale: J-I Qualifications & Experience: 1st Class 4-year BS(CS/IT) OR BE(EE) or equivalent from HEC recognized University/Institute with Network certification. At least 3 Years post qualification experience of designing, implementing and maintaining complex networks; capability to handle firewalls, routers, switches and other LAN/WAN equipment. Proficiency in installing, configuring and troubleshooting web, file, mail, DBMS, DNS and proxy servers etc. under Windows/Linux environments is required. Excellent command over spoken and written English. NETWORK ADMINISTRATOR [ABBOTTABAD,