Are women obligated to recite Pesukei Dezimra [i.e. Hodu-Yishtabach]?
The dispute: Some Poskim rule that women are obligated to recite Pesukei Dezimra just like men. Other Poskim rule that women are exempt from reciting Pesukei Dezimra, although are nevertheless allowed to do so if they wish, and they may choose to say even the opening and closing blessings of Baruch Sheamar and Yishtabach. The above applies for Ashkenazi women, and according to many Poskim, also for Sephardi women. Some Poskim, however, rule that since women are exempt from reciting Pesukei Dezimra, therefore, it is forbidden for women of Sephardic origin to recite the blessings of Baruch Sheamar and Yishtabach.
Practical directive: Practically, Admur rules like the middle opinion that the saying of Pesukei Dezimra is not obligatory for women. Nevertheless, it is a widespread custom amongst women of both Ashkenazi and Sephardic Jewry to initially recite the entire Pesukei Dezimra, just as a man, and so should initially be done. However, a woman who is pressed for time, such as a busy mother, may skip Pesukei Dezimra. Regarding the Sephardic custom: Some Sephardim follow the latter opinion and therefore the women do not recite Baruch Sheamar and Yishtabach with Hashem’s name upon reciting Pesukei Dezimra. Others however follow the middle opinion, and allow women to recite these blessings just like a man. Practically, whatever she chooses has upon him to rely, and she may continue with whatever custom she was brought up with.
 See Piskeiy Teshuvos 70:1
 M”B 70:2 based on Rebbe Akiva Eiger 52 who rules that one who skipped Pesukei Dezimra and Davened Shemoneh Esrei, and made amistake which requires him to repeat Shemoneh Esrei, is to recite Pesukei Dezimra with a blessing
 The reason: As the final ruling follows that women are obligated in the Shemoneh Esrei prayer [Admur 106:2] and since the recital of Pesukei Dezimra is for the sake of preparing for Shemoneh Esrei [Admur 51:1; 52:1; Tur 51; Brachos 32a], therefore women are also obligated in it. [M”B ibid]
 Admur 70:1 in parentheses “If they desire to say the other blessings of Kerias Shema, and Pesukei Dezimra and its blessings, they may.”; Implication of M”A 47:14 and Taz 47:10 that they are exempt from Pesukei Dezimra; Aruch Hashulchan 70:1 “Baruch Sheamar and Yishtabach is not an obligation upon them to say, although nevertheless they may say it, as why should they not be allowed to sing praise to Hashem as did Miriam and all the Jewish women by the splitting of the sea”; Pischei Olam 70:1; Kaf Hachaim 70:1
 The reason: As they are exempt from all time related commands. [See Admur ibid]
 The reason it is allowed for women to say a blessing despite them not being obligated in the command: Women are accustomed to say a blessing on even those commands that they are exempt from due to it being a Mitzvas Aseh Shehazman Grama. [Admur 589:2 regarding Shofar; 17:3 regarding Tzitzis; Rama 589:6; Taz 658:9; M”A 658:11; M”B 655:1; Rabbeinu Tam R”H 33a; Ran; Rosh in name of Mahritz Geios; Tur 589; Ritva Sukkah 2; Rashba 123; Maggid Mishneh Shofar 2 in name of Rashba; Shut Min Hashamayim 1; Birkeiy Yosef 654:2; Yosef Ometz 82; See Kaf Hachaim 17:4; 589:23] Women may say a blessing of “Asher Kidishana … Vitzivanu..” on commands that they are exempt from fulfilling, being that the men are commanded in this Mitzvah. Furthermore, although they do not receive as much reward as a man who is commanded in the Mitzvah, they do receive some reward and thus they too may say a blessing just like a man. [Admur 17:3]
 Kaf Hachaim 70:1 that so is the custom; Or Letziyon 2:86-18; Halichos Shlomo 7:2 in name of Rav SZ”A; Tzitz Eliezer 9:2; Michzeh Eliyahu 1:16; Piskeiy Teshuvos 70 footnote 6
The reason: As even according to those Sephardi Poskim who forbid women from saying blessings, it only applies by blessings of Mitzvos which contain the words “Asher Kidishanu” and not by blessings of praise. [See Magid Mishneh Sukkah 6:17; Tzelach Brachos 26b; Poskim ibid]
 Yabia Omer 2:6; 3:6; 8:8; 9:108; Yechaveh Daas 3:3; Halacha Berurah 52:7
The Sephardic custom regarding women saying blessings that they are exempt from: Some Poskim rule that women may never recite a blessing over any Mitzvah that they are not obligated in. [Michaber 589:6; Beis Yosef 589; Rambam Hilchos Tzitzis; Igur in name of Reb Yeshaya; Rashi, brought in Hagahos on Rambam; Chacham Tzevi] The Michaber ibid rules that they cannot say a blessing as Safek Brachos Lihakel. [Beis Yosef 589] The Birkeiy Yosef ibid states that after seeing the answer from heaven in Shut Min Hashamayim he retracted from ruling like the Michaber and would tell women to recite a blessing. He concludes that if the Michaber would have seen the Shut Min Hashamayim certainly he too would have retracted his ruling.
 Kaf Hachaim 70:1; 106:1
 Pashut from Admur, however according to those who follow the first opinion, which is that of the Mishneh Berurah, they would be required to recite Pesukei Dezimra even if they are pressed for time, and at the very least would need to recite Baruch Sheamar, Ashreiy and Yishtabach. [Halichos Bas Yisrael 2 footnote 21 in name of Rav Schineberg]
 Many Sephardim today follow the popular opinion of Rav Ovadia Yosef, and hence do not say the blessings
 Kaf Hachaim ibid that so is the custom
 Halichos Bas Yisrael 2:7